Question

A headhunter selects a sample of large companies and records the number of job openings at each. The data is as follows:
20, 18, 34, 27, 38, 26, 41, 29, 19

a) Calculate the sample mean.
b) Calculate the sample standard deviation.
c) Find the mode(s).
d) Find the 5 number summary.
e) Calculate the IQR.

Answer 1

a)

sample mean =28.00

b)

sample standard deviation =8.3367

c)

mode =does not exist , since all the values appears exactly once only

d)

minimum =18

quartile 1 =middle value of lower half (lower 4 values )=(19+20)/2=19.5

quartile 2 =middle value =(27+29)/2 =28

quartile 1 =middle value of upper half (top 4 values )=(34+38)/2=36

maximum value =41

therefore 5 number summary values are 18, 19.5 ,28, 36,41

e)

IQR =Q3-Q1 =36-19.5 =16.5