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In a population of five university students with GPAs of 2.5,2.3,1.7,1.4, and 1.1, a sample of three students are considered. What would be the standard deviation?

User Ryanve
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1 Answer

2 votes

Answer:

The standard deviation of the sample of GPAs is 0.59.

Explanation:

Let's calculate the standard deviation for the given sample of GPAs:

Step 1: Calculate the mean

Mean = (2.5 + 2.3 + 1.7 + 1.4 + 1.1) / 5 = 1.8

Step 2: Calculate the difference between each data point and the mean

(2.5 - 1.8), (2.3 - 1.8), (1.7 - 1.8), (1.4 - 1.8), (1.1 - 1.8)

= 0.7, 0.5, -0.1, -0.4, -0.7

Step 3: Square each difference

0.7^2, 0.5^2, (-0.1)^2, (-0.4)^2, (-0.7)^2

= 0.49, 0.25, 0.01, 0.16, 0.49

Step 4: Calculate the sum of squared differences

0.49 + 0.25 + 0.01 + 0.16 + 0.49 = 1.4

Step 5: Divide the sum of squared differences by the sample size minus one

1.4 / (5 - 1) = 0.35

Step 6: Take the square root of the result from step 5

√0.35 ≈ 0.59

Therefore,

The standard deviation of the sample of GPAs is 0.59.

User Pelerano
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