Question
Asked Sep 13, 2019
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The question is, for the following scores find the mean, median, sum of squared deviations, variance, and standard deviation. 2,2,0,5,1,4,1,3,0,,0,1,4,,4,0,1,,4,3,4,2,1,0. Tnank you!

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Expert Answer

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Step 1

The mean of the data is calculated as follows:

2 2 051+4 +1+3 +0+0 +1+4+4 +0 +1+ 4+3+4+2+1+0
21
Mean=
42
21
Il
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2 2 051+4 +1+3 +0+0 +1+4+4 +0 +1+ 4+3+4+2+1+0 21 Mean= 42 21 Il

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Step 2

Median is the middle most items. There are 21 items. Therefore, median is the 11th ((21+1)/2) item in the ordered arrangement (ascending or descending) of the data values.

The data in ascending order is as follows:

0,0,0,0,0,1,1,1,1,1,2,2,2,3,3,4,4,4,4,4,5.

Therefore, median is 2 (11th item in the ordered arrangement).

The sum of squared deviations is calculated as follows:

 

(2-2j+(2-2j- (0-2) + (5-2)
| -+(1-2)(4-2)(1-2) (3-2
|+(0-2)+ (0-2) (1-2 +(4-2
|-+(4-2)-(0-2)+(1-2)+ (4-2)
(3-2)j(4-2(2-2)j +(1-2)
(+0-2)
Sum of squared deviations from mean|
_
= 56
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(2-2j+(2-2j- (0-2) + (5-2) | -+(1-2)(4-2)(1-2) (3-2 |+(0-2)+ (0-2) (1-2 +(4-2 |-+(4-2)-(0-2)+(1-2)+ (4-2) (3-2)j(4-2(2-2)j +(1-2) (+0-2) Sum of squared deviations from mean| _ = 56

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Step 3

The sample variance is calculated...

1
Sample variance
56
21 1
56
20
= 2.8
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1 Sample variance 56 21 1 56 20 = 2.8

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