Question

1. A sample was taken of the salaries of 20 employees of a large company which is the competitor of the company from part 1 above.

28	31	34	35	37	41	42	42	42	47
49	49	52	52	60	61	67	72	75	77

1. Find two measures of central tendency for the given data.
2. Find two measures of variability for the given data.
3. Construct a box plot for the given data and compare it to the one you made in part 1 above.

Answer 1

Part a. Measures of central tendency

We have 3 central tendencies mean , mode and median.

mean = 49.65

Median = Median is middle observation of ordered data now we have middle value 47 and 49 so we take average of this to value to find middle = (47+49)/2 = 48

median = 48

Mode = 42    ( mode is most frequent observation here 42 repeated 3 times so it is mode)

Part b Measures of variability :

1. Range : Maximum value - minimum value = 77-28 = 49

Range : 49

2. IQR ( Interquartile range ) : Q3 - Q1

Q1 = First quartile = 39    (37+41/2 =39 Q1 is median of the first half part )

Q3 = 3rd quartile = 60.5 ( 60+61/2 = 60.5 , Q3 is median of the second part )

IQR = 60.5 -39 = 21.5

IQR = 21.5

part c

Box plot

Q2 represent median which is 48

Q1 and Q3 are first and third quartile using that we can see the variation of the data