Question

Please answer this question with details, Step-by-Step:

Find the mean, median, 20% trimmed mean, and the first and third quartile
Each of 16 tennis players measured the diameter with a ruler, and then compute the circumference of a tennis ball. The results (in cm) are as follows, in increasing order.

18.8, 18.9, 18.9, 19.6, 20.1, 20.4, 20.4, 20.4, 20.4, 20.5, 21.2, 22.0, 22.0, 22.0, 22.0, and 23.6

Answer 1

#x=circumference of a tennis ball.

>x=c( 8.8, 18.9, 18.9, 19.6, 20.1, 20.4, 20.4, 20.4, 20.4, 20.5, 21.2, 22.0, 22.0, 22.0, 22.0,23.6)
> mean(x)
[1] 20.075

#mean=20.075
> median(x)
[1] 20.4

#Median=20.4

#Trimmed mean
> mean(x, trim = 0.2)
[1] 20.7

#20 % Trimmed mean is 20.7
#Q1=first quartile
> Q1=quantile(x,0.25);Q1
25%
19.975

#Q1=19.975

#Q3=third quartile
> Q3=quantile(x,0.75);Q3
75%
22

#Q3=22