In one of the first statistical textbooks, Arthur Bowley (1901) used these data to illustrate an arithmetic and graphical analysis of time-series data using the total value of British and Irish exports from 1855-1899. He presented a line graph of the time-series data, supplemented by overlaid line graphs of 3-, 5- and 10-year moving averages. His goal was to show that while the initial series showed wide variability, moving averages made the series progressively smoother.

1 |

A data frame with 45 observations on the following 2 variables.

`Year`

Year, from 1855-1899

`Value`

total value of British and Irish exports (millions of Pounds)

Bowley, A. L. (1901). *Elements of Statistics*. London: P. S. King and Son,
p. 151-154.

Digitized from Bowley's graph.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
data(Bowley)
# plot the data
with(Bowley,plot(Year, Value, type='b',
ylab="Value of British and Irish Exports",
main="Bowley's example of the method of smoothing curves"))
# find moving averages-- use center alignment (requires width=ODD)
require(gtools, warn.conflicts=FALSE)
mav3<-running(Bowley$Value, width=3, align="center")
mav5<-running(Bowley$Value, width=5, align="center")
mav9<-running(Bowley$Value, width=9, align="center")
lines(Bowley$Year[2:44], mav3, col='blue', lty=2)
lines(Bowley$Year[3:43], mav5, col='green3', lty=3)
lines(Bowley$Year[5:41], mav9, col='brown', lty=4)
# add lowess smooth
lines(lowess(Bowley), col='red', lwd=2)
require(ggplot2, warn.conflicts=FALSE)
qplot(Year,Value, data=Bowley)+geom_smooth()
``` |

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