Question

The test scores of 15 employees are listed. Use this data set to answer the questions below.

13    9    18    15    14    21    7    10    11

20    5    18    37    16    17

What is the mean?

What is the median?

What is the standard deviation?

What is the variance?

What is the range?

Answer 1

Solution:

x	x2
13	169
9	81
18	324
15	225
14	196
21	441
7	49
10	100
11	121
20	400
5	25
18	324
37	1369
16	256
17	289
x=231	x2=4369

The sample mean is

Mean = (x / n) )

=13+9+18+15+14+21+7+10+11+20+5+18+37+16+17/15

=231/15

=15.4

Mean = 15.4

Median :
Observations in the ascending order are :
5,7,9,10,11,13,14,15,16,17,18,18,20,21,37

Here, n=15 is odd.

M= value of (n+12)th observation

= value of (15+12)th observation

= value of 8th observation

=15

Median = 15

The sample standard is S

  S =( x2 ) - (( x)2 / n ) n -1

=4369-(231)215/14

=4369-3557.4/14

=811.6/14

=57.9714

=7.6139

The sample standard = 7.61

The variance = S2

  S2 =( x2 ) - (( x)2 / n ) n -1

=4369-(231)215/14

=4369-3557.4/14

=811.6/14

=57.9714
The variance =57.97

Range = Maximum value + Minimum value

= 37 + 5

= 32

Range = 32