Question

The most frequently used measures of central tendency for quantitative data are the mean and the median. The following table shows civil service examination scores from 24 applicants to law enforcement jobs:

83        74        85        79

82        67        78        70

18        93        64        27

93        98        82        78

68        82        83        99

96        62        93        58

Using Excel, find the mean, standard deviation, and 5-number summary of this sample.

• Construct and paste a box plot depicting the 5-number summary.
• Does the dataset have outliers? If so, which one(s)?
• Would you prefer to use the mean or the medianas this dataset’s measure of central tendency? Why?

Answer 1

Mean value for given data is

Create the following table.

data	data-mean	(data - mean)2
83	7.5	56.25
74	-1.5	2.25
85	9.5	90.25
79	3.5	12.25
82	6.5	42.25
67	-8.5	72.25
78	2.5	6.25
70	-5.5	30.25
18	-57.5	3306.25
93	17.5	306.25
64	-11.5	132.25
27	-48.5	2352.25
93	17.5	306.25
98	22.5	506.25
82	6.5	42.25
78	2.5	6.25
68	-7.5	56.25
82	6.5	42.25
83	7.5	56.25
99	23.5	552.25
96	20.5	420.25
62	-13.5	182.25
93	17.5	306.25
58	-17.5	306.25

Find the sum of numbers in the last column to get.

So

The minimum is the smallest value in a data set.

Ordering the data from least to greatest, we get:

18   27   58   62   64   67   68   70   74   78   78   79   82   82   82   83   83   85   93   93   93   96   98   99   

So, the minimum is 18.

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

18   27   58   62   64   67   68   70   74   78   78   79   82   82   82   83   83   85   93   93   93   96   98   99   

So, the bottom half is

18   27   58   62   64   67   68   70   74   78   78   79   

The median of these numbers is 67.5.

planation

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

18   27   58   62   64   67   68   70   74   78   78   79   82   82   82   83   83   85   93   93   93   96   98   99   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median=

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

18   27   58   62   64   67   68   70   74   78   78   79   82   82   82   83   83   85   93   93   93   96   98   99   

So, the upper half is

82   82   82   83   83   85   93   93   93   96   98   99   

The median of these numbers is 89.

The maximum is the greatest value in a data set.

Ordering the data from least to greatest, we get:

18   27   58   62   64   67   68   70   74   78   78   79   82   82   82   83   83   85   93   93   93   96   98   99   

So, the maximum is 99.

Hence there are 2 outliers: 18 and 27

As there are outliers so median is to used for measure of central tendency