split_var: Split numeric variables into smaller groups

Description Usage Arguments Details Value Note See Also Examples

View source: R/split_var.R

Description

Recode numeric variables into equal sized groups, i.e. a variable is cut into a smaller number of groups at specific cut points. split_var_if() is a scoped variant of split_var(), where transformation will be applied only to those variables that match the logical condition of predicate.

Usage

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split_var(
  x,
  ...,
  n,
  as.num = FALSE,
  val.labels = NULL,
  var.label = NULL,
  inclusive = FALSE,
  append = TRUE,
  suffix = "_g"
)

split_var_if(
  x,
  predicate,
  n,
  as.num = FALSE,
  val.labels = NULL,
  var.label = NULL,
  inclusive = FALSE,
  append = TRUE,
  suffix = "_g"
)

Arguments

x

A vector or data frame.

...

Optional, unquoted names of variables that should be selected for further processing. Required, if x is a data frame (and no vector) and only selected variables from x should be processed. You may also use functions like : or tidyselect's select-helpers. See 'Examples' or package-vignette.

n

The new number of groups that x should be split into.

as.num

Logical, if TRUE, return value will be numeric, not a factor.

val.labels

Optional character vector, to set value label attributes of recoded variable (see vignette Labelled Data and the sjlabelled-Package). If NULL (default), no value labels will be set. Value labels can also be directly defined in the rec-syntax, see 'Details'.

var.label

Optional string, to set variable label attribute for the returned variable (see vignette Labelled Data and the sjlabelled-Package). If NULL (default), variable label attribute of x will be used (if present). If empty, variable label attributes will be removed.

inclusive

Logical; if TRUE, cut point value are included in the preceding group. This may be necessary if cutting a vector into groups does not define proper ("equal sized") group sizes. See 'Note' and 'Examples'.

append

Logical, if TRUE (the default) and x is a data frame, x including the new variables as additional columns is returned; if FALSE, only the new variables are returned.

suffix

Indicates which suffix will be added to each dummy variable. Use "numeric" to number dummy variables, e.g. x_1, x_2, x_3 etc. Use "label" to add value label, e.g. x_low, x_mid, x_high. May be abbreviated.

predicate

A predicate function to be applied to the columns. The variables for which predicate returns TRUE are selected.

Details

split_var() splits a variable into equal sized groups, where the amount of groups depends on the n-argument. Thus, this functions cuts a variable into groups at the specified quantiles.

By contrast, group_var recodes a variable into groups, where groups have the same value range (e.g., from 1-5, 6-10, 11-15 etc.).

split_var() also works on grouped data frames (see group_by). In this case, splitting is applied to the subsets of variables in x. See 'Examples'.

Value

A grouped variable with equal sized groups. If x is a data frame, for append = TRUE, x including the grouped variables as new columns is returned; if append = FALSE, only the grouped variables will be returned. If append = TRUE and suffix = "", recoded variables will replace (overwrite) existing variables.

Note

In case a vector has only few number of unique values, splitting into equal sized groups may fail. In this case, use the inclusive-argument to shift a value at the cut point into the lower, preceeding group to get equal sized groups. See 'Examples'.

See Also

group_var to group variables into equal ranged groups, or rec to recode variables.

Examples

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data(efc)
# non-grouped
table(efc$neg_c_7)

# split into 3 groups
table(split_var(efc$neg_c_7, n = 3))

# split multiple variables into 3 groups
split_var(efc, neg_c_7, pos_v_4, e17age, n = 3, append = FALSE)
frq(split_var(efc, neg_c_7, pos_v_4, e17age, n = 3, append = FALSE))

# original
table(efc$e42dep)

# two groups, non-inclusive cut-point
# vector split leads to unequal group sizes
table(split_var(efc$e42dep, n = 2))

# two groups, inclusive cut-point
# group sizes are equal
table(split_var(efc$e42dep, n = 2, inclusive = TRUE))

# Unlike dplyr's ntile(), split_var() never splits a value
# into two different categories, i.e. you always get a clean
# separation of original categories
library(dplyr)

x <- dplyr::ntile(efc$neg_c_7, n = 3)
table(efc$neg_c_7, x)

x <- split_var(efc$neg_c_7, n = 3)
table(efc$neg_c_7, x)

# works also with gouped data frames
mtcars %>%
  split_var(disp, n = 3, append = FALSE) %>%
  table()

mtcars %>%
  group_by(cyl) %>%
  split_var(disp, n = 3, append = FALSE) %>%
  table()

Example output

sh: 1: cannot create /dev/null: Permission denied
sh: 1: wc: Permission denied
Could not detect number of cores, defaulting to 1.

  7   8   9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  27 
 75  99 106 120  96  85  64  54  45  30  35  26  16  16   2   7   4   3   6   1 
 28 
  2 

  1   2   3 
280 301 311 
    neg_c_7_g pos_v_4_g e17age_g
1           2         2        3
2           3         1        3
3           2         2        2
4           2         3        1
5           2         3        3
6           3         1        3
7           3         2        1
8           2         3        3
9           3         2        2
10          2         2        3
11          3         1        1
12          3         1        3
13          3         3        2
14          3         3        2
15          3         1        2
16          3         3        3
17          2         3        2
18          2         2        1
19          3         2        3
20          3         2        2
21          2         1        3
22          1         2        1
23          1         3        3
24          3         3        3
25          2         3        3
26          3         2        2
27       <NA>         1        3
28          2         1        2
29          3         1        3
30          2      <NA>        3
31          3         2        3
32          1         2        3
33          3         1        3
34          3         2        2
35          1         3        2
36          2         3        2
37          3         1        1
38          1         3        3
39          3         3        3
40          3         2        3
41          3         2        3
42          3         3        1
43          3         1        1
44          3         1        1
45          3         2        1
46       <NA>         1        2
47          3         1        1
48          3         2        1
49          3         3        2
50          3         1        3
51          3         3        1
52          2      <NA>        2
53          3         1        1
54          3         1        1
55          1         3        2
56          2         3        3
57          3      <NA>     <NA>
58       <NA>         1        2
59          3         1        2
60          3         1        1
61          3         3        3
62          3         3        3
63          1         3        3
64          3         1        1
65          2      <NA>        3
66          3         3        3
67          3         1        2
68          2         2        2
69          3      <NA>        2
70          3         1        1
71          1         3        2
72          3         2     <NA>
73          2         2        3
74          3         1        1
75          2         3        3
76          2         2        2
77          3         1        1
78          2         2        3
79          2         1        2
80          3         1        2
81          1         3        2
82          3         2     <NA>
83          2         3        2
84          3         1        2
85          2         3        2
86          3         3        2
87          3         1        1
88          3         2        1
89          3         1        2
90          2      <NA>        3
91          2         2        2
92          2         3        2
93          3         2        1
94          2         3        3
95          2         2        1
96          3      <NA>        3
97          2      <NA>        1
98          2         1        3
99          2         3        3
100         3         1        2
101         3         1        2
102         2         1        1
103         2         3        2
104         1         1        2
105         3         2        3
106         3         2        1
107         2         3        2
108         2         2        2
109         3         2        2
110         3         2        2
111         2         3        1
112         2         1        2
113         3         1        3
114         1         3        2
115         3         2        1
116         3         2        3
117         2         2        3
118         3         2        2
119         3         1        1
120         3         1        3
121         1         3        3
122         3      <NA>        1
123         3      <NA>        3
124         3         1        1
125         3         2        3
126         3         2        1
127         1      <NA>        2
128         3      <NA>        3
129         1         3        3
130         3         3        1
131         3         1        3
132         1         3        2
133         3         2        2
134      <NA>      <NA>        2
135         3         1        3
136         2         2        3
137         3         2        3
138         1         3        2
139         2         3        2
140         2         3        3
141         3         1        2
142         2         1        3
143         3         1        3
144      <NA>      <NA>        3
145         2         2        3
146         2         3        3
147      <NA>         2        1
148         2         1        1
149         2         2        2
150         3         2        3
151         2         3        3
152         3         2        3
153         2         2        3
154         2         3        3
155         2         3        1
156         2         2        1
157         1         2        2
158         3         3        3
159         2         2        2
160         2         2        1
161         3         1        2
162         3         2        3
163         3         1        3
164         2         1     <NA>
165         2         3        2
166         3         3        1
167      <NA>      <NA>        3
168         3      <NA>        2
169         2         1        2
170         2      <NA>        2
171         1         3        1
172         2         3        3
173         1         3        2
174         2         3        1
175         2         3        3
176         2         2        1
177         2         1        3
178         3         2        3
179         1         2        3
180         2         3        2
181         2         3        3
182         2         2        3
183         3         1        2
184         2         2        2
185         3      <NA>        2
186         3         3        2
187      <NA>         3        1
188         3         1        3
189         1         2        2
190         2         3        1
191         3         2        2
192         3         3     <NA>
193         2         1        3
194         2         2        1
195         1         3        3
196         1         3        2
197         3      <NA>        3
198         3      <NA>        3
199         3         1        3
200         1         2        3
201         1         3        3
202         3         1        3
203         1         3        3
204         3         1        3
205         1         3        3
206         1         2        2
207         3         2        3
208         2         3        3
209         2         3        3
210         2         2        3
211         2         2        3
212         3         1        3
213         1         2        2
214         3         1        3
215         3         3        1
216         1         3        3
217         3         3        3
218         3         1        2
219         2         3        2
220         1         3        1
221         2         1        3
222         3         2        3
223         2         2        3
224         2         2        3
225         3         2        3
226         1         1        2
227         3         3        3
228         3         1        3
229         2         3        1
230         3         2        1
231         3         3        3
232         3         2        3
233         2         3        3
234         2         1        3
235         2         2        3
236         2         1        3
237         2         3        1
238         2         2        2
239         1         3        2
240         2         3        2
241         1         2        2
242         2         2        2
243         2         1        3
244         2         2        3
245         1         2        3
246         2         3        2
247         1         2        2
248         1         1        3
249         2         3        3
250         2         1        3
251         2         1        2
252         2         1        2
253         3         3        1
254         2         1        1
255         2         1        3
256         3         1        3
257         2         3        1
258         3         1        3
259         2         2        3
260         3         2        3
261         1         2        2
262         3         3        3
263         2         1        3
264         2         2        2
265         1         3        3
266         2         2        2
267         3         1        1
268      <NA>         1        3
269         2         2        3
270         3         1        2
271         1         2        2
272         2         1        1
273         1         1        2
274         2         2        1
275         3         1        1
276         2         2        2
277         1         2        2
278         1         2        1
279         1         3        1
280         1         3        1
281         1         3        1
282         1         3        1
283         1         3        1
284         2         3        1
285         1         3        2
286         2         3        1
287         2         1        3
288         1         3        3
289         3         1        3
290         3         1        1
291         2         1        3
292         1         3        3
293         1         1        2
294         1         3        2
295         1         2        3
296         1         2        1
297         3         2        1
298         1         2        2
299         2         2        1
300         1         3        1
301         3         2        3
302         1         1        1
303         3         1        2
304         3         3        3
305         1         3        2
306         3         3        3
307         3         2        3
308         1         2        2
309         1         1        1
310         1         3        1
311         3         2        3
312         3         1        1
313         3         1        1
314         1         3        3
315         2         2        1
316         3         2        1
317         2         1        1
318         3         1        2
319         2         1        3
320         1         3        3
321         2         3        3
322         1         3        3
323         1         3        3
324         2         2        3
325         1         2        3
326         2         2        3
327         3         2        3
328         3         1        2
329         1         3        2
330         2         1     <NA>
331         2         2        2
332         2         2        2
333         3         3        3
334         2         3        3
335         1         3        3
336         1         3        1
337         3         1        3
338         1         3        3
339         3         2        3
340         1         3        2
341         1         3        1
342         3         3        1
343         1         1        2
344         1         3     <NA>
345         1         2        2
346         1         2        3
347         1         2        1
348         3         1        3
349         1         3        2
350         1         3        3
351         1         1        2
352         1         3        3
353         2         1        2
354         2         2        2
355         2         1        1
356         3         1        2
357         1         2        3
358         2         2        1
359         3         1        2
360         1         2        3
361         2         2        3
362         1         1        2
363         1         3        2
364         2         3        1
365         1         2        1
366         1         3        1
367         1         3        1
368         2         2        2
369         2         1        2
370         1         3        2
371         1         3        3
372         2         2        3
373         3         2        3
374         3         1        2
375         2         2        3
376         3         1        2
377         2         2        1
378         1         3        2
379         1         2        1
380         2         1        2
381         3         1        1
382         2         1        1
383         3         2        2
384         3         1        3
385         1         3        2
386         1         2        1
387         1         3        2
388         3         3        3
389         2         3        3
390         3         1        2
391         3         1        3
392         2         2        3
393         1         2        1
394         3         2        1
395         3         2        2
396         3         2        1
397         3         1        2
398         3         1        2
399         3         2        1
400         1         3        2
401         2         2        2
402         2         2        1
403         3         1        3
404         2         3        3
405         3         2        1
406         2         1        2
407         1         2        2
408         1         2        3
409         2         1        3
410         3         2        3
411         3         3        3
412         1         1        1
413         2         2        1
414         2         2        1
415         1         2        1
416         2         2        1
417         3         1        1
418         2         2        1
419         3         1        1
420         2         2        3
421         3         2        3
422         2         2        2
423         3         3        2
424         2         2        3
425         2         1        3
426         3         1        1
427         2         2        2
428         2         3        2
429         2         3        3
430         2         3        3
431         1         1        1
432         3         1        2
433         2         2        3
434         2         2        2
435         3         1        3
436         3         2        2
437         3         1        2
438         2         2        2
439         1         3        1
440         3         1        3
441         2         1        2
442         3         3        2
443         3         3        1
444         2         2        3
445         3         1        3
446         2         2        2
447         2         2        3
448         2         1     <NA>
449         3         1        3
450         3         2        1
451         1         3        1
452         2         2        2
453         1         3        2
454         1         3        2
455         1         2        3
456         3         1        2
457         1         3        2
458         1         2        3
459         1         3        3
460         2         3        2
461         1         2        3
462         2         3        2
463         2         2        3
464         3         1        3
465         3         2        2
466         3         2        3
467         3         2        2
468         1         3        2
469         1         2        1
470         1         2        2
471         3         2        3
472         1         3        1
473         2         2        2
474         1         3        3
475         1         3        1
476         1         3        2
477         2         1        1
478         3         2        1
479         1         3        1
480         2         2        2
481         3         3        1
482         1         1        2
483         1         3        2
484         1         3        2
485         2         2        2
486         2         3        2
487         3         3        3
488         1         1        3
489         1         3        1
490         1         2        3
491         2         2        2
492         1         2        1
493         2         2        3
494         2         1        2
495         3         1     <NA>
496         2         2        2
497         1         2        3
498         2         1        2
499         3         1        1
500         2         2        2
501         3         2        1
502         1         2        2
503         1         2        1
504         3         2        3
505         2         1        2
506         3         1        3
507         3         1        1
508         3         1        1
509         3         1        1
510         3         1        3
511         2         2        2
512         3         1        2
513         3         3        1
514         1         3        3
515         1         3        3
516         3         1        1
517         1         3        3
518         3      <NA>        2
519         3         2        1
520         2         2        2
521         1         2        1
522         3         3        3
523         1         2        1
524         2         2        2
525         1         3        2
526         2         1        2
527         1         1        3
528         1         3        2
529         2         1        2
530         1         3        3
531         3         1        3
532         1         3        1
533         2         2        2
534         1         2        3
535         1         2        2
536         1         2        1
537         2         2        3
538         1         1        3
539         3         1        2
540         2         2        3
541      <NA>         2        3
542         1         3        3
543         1         3        2
544         1         2        1
545         1         3        1
546         1         3        1
547         1         3        1
548         3         2        2
549         3         1        2
550         1         1        2
551         1         3        1
552         1         3        2
553         2         2        3
554         1         3        3
555         1         2        1
556         1         3        1
557         3         3        2
558         3         3        3
559         3         3        2
560         3         3        1
561         3         3        2
562         2         3        3
563         3         2        1
564         1         1        3
565         1         3        1
566         1         3        3
567         1         3        3
568         1         3        1
569         3         2     <NA>
570         3         1        3
571         3         1        1
572         3         2        2
573         3         1        3
574         3         1        2
575         3         1        3
576         2         2        2
577         2         1        3
578         3         1        1
579         1         3        2
580         3         1        1
581         2         3        2
582         3         1        3
583         3         1        3
584         3         1        3
585         2         2        1
586         3         1        2
587         2         2        3
588         2         2        2
589         2         2        2
590         1         3        1
591         1         2        3
592         3         1        3
593         3         1        3
594         2         3        1
595         1         3        1
596         3         1        3
597         3         1        1
598         2         1        1
599         3         1        3
600         3         2        3
601         3         2        3
602         2         2        3
603         3         1        2
604         1         3        2
605         1         3        2
606         2         1        3
607         3         2        1
608         3         1        1
609         3         2        2
610         1         3        2
611         2         3        1
612         2         2        1
613         3         1        1
614         2         3        1
615         3         2        3
616         1         1     <NA>
617         1         3        3
618         1         3        1
619         1         2        2
620         3         3        3
621         2         1        2
622         1         2        2
623         1         1        3
624         2         3        1
625         3         1        3
626         1         3        1
627         2         3        1
628         2         3        3
629         2         3        3
630         2         3        3
631         2         2        2
632         2         1        1
633         1         1        1
634         3         1        2
635         3         1        3
636         1         1        1
637         1         2        1
638         1         2        2
639         1         3        3
640         3         1        1
641         3         1        3
642         3         3        1
643         1         3        2
644         2         3        2
645         1         3        1
646         2         2        1
647         2         2        2
648         2         2        2
649         2         2        1
650         2         2        2
651         2         3        1
652         2         3        3
653         2         1        1
654         3         1        3
655         1         3        1
656         1         3        2
657         2         3        1
658         1         3        2
659         1         3        2
660         3         3        2
661         2         3        2
662         2         2        1
663         3         1        2
664         1         2        1
665         2         2        2
666         3         2        1
667         2         2        1
668         1         1        3
669         2         2        1
670         2         2        1
671         2         1        1
672         1         1        2
673         2         1        1
674         1         3        1
675         3         1        2
676         2         2        1
677         1         3        3
678         2         2        3
679         1         2        1
680         1         3        3
681         1         3        1
682         1         3        1
683         1         3        2
684         1         3        3
685         1         2        3
686         2         2        1
687         1         2        1
688         2         2        1
689         2         2        1
690         2         2        2
691         1         3        2
692         3         2        2
693         2         2        2
694         2         2        1
695         1         3        3
696         2         2        3
697         3         1        1
698         2         1        3
699         2         2        3
700         3         1        3
701         3         1        1
702         2         2        1
703         3         2        1
704         1         2        3
705         2         2        2
706         3         2        3
707         1         1        1
708         1         2        2
709         2         1        1
710         1         2        1
711         1         2        3
712         3         2        1
713         2         1        1
714         3         2        1
715         2         2        1
716         3         2        2
717         3         2        2
718         1         1        1
719         1         3        1
720         3         1        3
721         1         3        1
722         2         3        1
723         1         2        3
724         3         1        2
725         3         1        2
726         3         1        3
727         3         1        2
728         2         1        2
729         3         1        3
730         2         2        2
731         2         2        2
732         3         1        2
733         2         3        2
734         2         3        3
735         2         3        1
736         2         2        3
737         2         1        1
738         1         3        2
739         3         3        3
740         1         3        3
741         3         3        3
742         1         2        2
743         3         1        3
744         2         2        2
745         2         1        3
746         2         2        2
747         1         1        2
748         2         1        2
749         3         3        3
750         3         2        3
751         1         3        2
752         1         3        3
753         3         2        3
754         2         2        3
755         2         1        2
756         2         2        1
757         1         3        2
758         1         3        3
759         3         1        3
760         1         3        1
761         1         3        1
762         3         1        3
763         1         3        2
764         3         1        3
765         1         3        2
766         1         3        3
767         3         1        1
768         1         3        1
769         1         3        1
770         1         3        2
771         1         3        3
772         1         2        2
773         1         2        3
774         1         2        3
775         1         3        3
776         3         1        1
777         2         1        3
778         2         1        1
779         3         1        1
780         2         2        2
781         1         1        2
782         2         1        1
783         1         3        1
784         1         1        1
785         3         1        2
786         2         2        2
787         3         1        1
788         2         2        1
789         2         2        3
790         1         3        1
791         2         3        1
792         2         1        1
793         1         1        1
794         3         1        3
795         1         3        3
796         2         1        2
797         3         2        3
798         2         2        1
799         2         1        2
800         3         3        3
801         1         3        3
802         3         3        2
803         3         3        2
804         3         2        1
805         1         3        2
806         2         3        2
807         1         3        2
808         1         3        3
809         1         3        3
810         1         3        3
811         1         2        2
812         1         2        2
813         1         2        1
814         3         1        2
815         1         2        1
816         2         2        2
817         3         1        2
818         2         1        3
819         1         3        1
820         2         1        1
821         1         2        1
822         3         2        1
823         3         2        1
824         3         1        1
825         3         3        1
826         3         3        1
827         3         3        1
828         2         1        2
829         3         1        1
830         2         2        1
831         2         3        3
832         2         3        2
833         1         3        2
834         2         1        3
835         2         1        1
836         2         1        1
837         2         1        1
838         1         2        3
839         1         3        1
840         3         3        1
841         3         3        3
842         2         3        3
843         1         3        2
844         2         3        2
845         1         2        1
846         1         1        1
847         1         3        3
848         1         1        2
849         2         2        2
850         1         3        2
851         1         2        1
852         2         3        1
853         2         2        3
854         1         3        2
855         2         3        3
856         1         3        3
857         2         3        3
858         2         1        1
859         3         1        3
860         1         2        1
861         1         3        2
862         2         3        1
863         2         2        2
864         2         1        3
865         2         2        3
866         1         3        2
867         1         2        2
868         1         3        1
869         2         2        1
870         1         3        2
871         1         3        1
872         1         2        2
873         1         1        1
874         1         1        2
875         1         3        2
876         3         1        1
877         3         1        3
878         2         1        2
879         3         1        1
880         1         1        2
881         1         1        3
882         1         1        1
883         2         1        2
884         3         1        3
885         3         1        1
886         3         2        2
887         3         1        2
888         1         3        1
889         2         2        1
890         3         1        3
891         1         3        1
892         1         2        2
893         3         3        2
894         3         1        3
895         2         1        3
896         3         1        3
897         3         1        1
898         1         3        2
899         1         2        2
900         3         3        1
901         2         3        1
902         2         2        1
903      <NA>      <NA>     <NA>
904      <NA>      <NA>     <NA>
905      <NA>      <NA>     <NA>
906      <NA>      <NA>     <NA>
907      <NA>      <NA>     <NA>
908      <NA>      <NA>     <NA>

# Negative impact with 7 items (neg_c_7_g) <categorical> 
# total N=908  valid N=892  mean=2.03  sd=0.81
 
  val frq raw.prc valid.prc cum.prc
    1 280   30.84     31.39   31.39
    2 301   33.15     33.74   65.13
    3 311   34.25     34.87  100.00
 <NA>  16    1.76        NA      NA

# Positive value with 4 items (pos_v_4_g) <categorical> 
# total N=908  valid N=881  mean=2.03  sd=0.81
 
  val frq raw.prc valid.prc cum.prc
    1 275   30.29     31.21   31.21
    2 304   33.48     34.51   65.72
    3 302   33.26     34.28  100.00
 <NA>  27    2.97        NA      NA

# elder' age (e17age_g) <categorical> 
# total N=908  valid N=891  mean=2.05  sd=0.82
 
  val frq raw.prc valid.prc cum.prc
    1 274   30.18     30.75   30.75
    2 294   32.38     33.00   63.75
    3 323   35.57     36.25  100.00
 <NA>  17    1.87        NA      NA


  1   2   3   4 
 66 225 306 304 

  1   2 
291 610 

  1   2 
597 304 

Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

    x
       1   2   3
  7   75   0   0
  8   99   0   0
  9  106   0   0
  10  18 102   0
  11   0  96   0
  12   0  85   0
  13   0  14  50
  14   0   0  54
  15   0   0  45
  16   0   0  30
  17   0   0  35
  18   0   0  26
  19   0   0  16
  20   0   0  16
  21   0   0   2
  22   0   0   7
  23   0   0   4
  24   0   0   3
  25   0   0   6
  27   0   0   1
  28   0   0   2
    x
       1   2   3
  7   75   0   0
  8   99   0   0
  9  106   0   0
  10   0 120   0
  11   0  96   0
  12   0  85   0
  13   0   0  64
  14   0   0  54
  15   0   0  45
  16   0   0  30
  17   0   0  35
  18   0   0  26
  19   0   0  16
  20   0   0  16
  21   0   0   2
  22   0   0   7
  23   0   0   4
  24   0   0   3
  25   0   0   6
  27   0   0   1
  28   0   0   2
.
 1  2  3 
11 10 11 
.
 1  2  3 
10  8 14 

sjmisc documentation built on Dec. 11, 2021, 9:34 a.m.