Calculate the 5 number summary and the interquartile range o

Calculate the 5 number summary and the interquartile range of the following data: 25, 59, 43, 33, 37, 5, 30, 29, 15, 11, 47, 40, 23, 56, 32 Q1 = Q2 = Q3 = Min = Max = IQR

Solution

Ordering the data,

5
11
15
23
25
29
30
32
33
37
40
43
47
56
59

Thus, we have the lower half:

5
11
15
23
25
29
30
32

And upper half:

32
33
37
40
43
47
56
59

Thus,

Q1 = median of lower half =    24
Q2 = Median = 32
Q3 = median of upper half =    41.5

Minimum =    5
Maximum =    59

IQR = Q3 - Q1 =    17.5