(a) Find Mean, Median and Mode.

(b) Show a boxplot of the data. Clearly indicating the five-number summary.

Given :-

11,13,13,15,15,16,19,20,20,20,21,21,22,23,24,30,40,45,45,45,71,72,73,75

A)

(i) Mean:-

Mean (x´) = (sum of all elements in data) / (no of elements in data)

(x´) = ( 11+13+13+15+15+16+19+20+20+20+21+21+22+23+24+30+40+45+45+45+71+72+73+75) / (24) $= \frac{769}{24}$ $=32.04166$

(ii) Median; - The middle number in a given sequence of data, taken as the average of the two middle numbers when the sequence has an even number of data

Here we have even no. so median will be

$\frac{(21+22)}{2} = 21.5$

(iii) mode:- The number which appears most Frequent in a set of Data.

Here mode is 45 & 20 with occurrence of 3

B)Box plot

For plotting box plot divide the given data in 3 segments

First segment only contains median and other two segments will contain upper and lower part of median

median=21.5

upper segment =22,23,24,30,40,45,45,45,71,72,73,75

lower segment =11,13,13,15,15,16,19,20,20,20,21,21

Find out mean of each segment and mark it on graph as shown bellow and also mark actual median of data

median of upper segment =45

median of lower segment =17.5

plot the chart