What is the value of the standard deviation of the following set of scores? X: 4, 10, 7, 6, 6, 9
a. 4.8
b. 2
c. 4
d. 2.19
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To find the standard deviation, we first need to calculate the mean of the set of scores:
Mean = (4 + 10 + 7 + 6 + 6 + 9) / 6
Mean = 42 / 6
Mean = 7
Next, we calculate the sum of the squared differences between each score and the mean:
(4-7)^2 + (10-7)^2 + (7-7)^2 + (6-7)^2 + (6-7)^2 + (9-7)^2
= 3^2 + 3^2 + 0^2 + 1^2 + 1^2 + 2^2
= 9 + 9 + 0 + 1 + 1 + 4
= 24
Then, we divide this sum by the number of scores minus 1 and take the square root:
Standard deviation = sqrt(24 / (6-1))
Standard deviation = sqrt(24 / 5)
Standard deviation = sqrt(4.8)
Standard deviation ≈ 2.19
Therefore, the value of the standard deviation of the set of scores is approximately 2.19, which corresponds to option d.
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