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Answer:
(1) Variance = 4.5 and Standard deviation = 2.121.
(2) Variance = 4.5 and Standard deviation = 2.121.
(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged.
Step-by-step explanation:
We are given with the following set of data below;
X
5 5 - 8 = -3 9
5 5 - 8 = -3 9
8 8 - 8 = 0 0
10 10 - 8 = 2 4
10 10 - 8 = 2 4
10 10 - 8 = 2 4
9 9 - 8 = 1 1
9 9 - 8 = 1 1
<u> 6 </u> 6 - 8 = -2 <u> 4 </u>
Total <u> 72 </u> <u> 36 </u>
<u>Firstly, the mean of the above data is given by;</u>
Mean, =
= = 8
(1)Now, the variance of the given data is;
Variance =
= = 4.5
So, the standard deviation, (S.D.) =
= = 2.12
(2) Now, each value is added by 2; so the new data set is given by;
X
7 7 - 10 = -3 9
7 7 - 10 = -3 9
10 10 - 10 = 0 0
12 12 - 10 = 2 4
12 12 - 10 = 2 4
12 12 - 10 = 2 4
11 11 - 10 = 1 1
11 11 - 10 = 1 1
<u> 8 </u> 8 - 10 = -2 <u> 4 </u>
Total <u> 90 </u> <u> 36 </u>
<u>Firstly, the mean of the above data is given by;</u>
Mean, =
= = 10
(1)Now, the variance of the given data is;
Variance =
= = 4.5
So, the new standard deviation, (S.D.) =
= = 2.12
(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged as we see in the case of variance or standard deviation.