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.