Question

Find the standard deviation of the following sample data set: {75, 65, 100, 80, 85, 75, 100}

A) 12.5
B) 13
C) 13.5
D) 14

Answer 1

The standard deviation of the sample data set {75, 65, 100, 80, 85, 75, 100} is approximately 14, which corresponds to option D.

Step-by-step explanation:

To find the standard deviation of the sample data set {75, 65, 100, 80, 85, 75, 100}, we will follow these steps:

1. Calculate the mean (average) of the sample.
2. Subtract the mean from each data value and square the result.
3. Find the sum of all the squared values.
4. Divide by the sample size minus one to get the variance.

Take the square root of the variance to get the standard deviation.
Firstly, let's calculate the mean of the sample:
(75 + 65 + 100 + 80 + 85 + 75 + 100) / 7 = 82.8571 approximately.
Next, we calculate each value's deviation from the mean, square it, and sum all the squared deviations:
((75-82.8571)^2 + (65-82.8571)^2 + (100-82.8571)^2 + (80-82.8571)^2 + (85-82.8571)^2 + (75-82.8571)^2 + (100-82.8571)^2) = 1200.
Then we divide the sum by the sample size minus one (n-1), where n is the number of samples, which in this case is 7:
1200 / (7-1) = 1200 / 6 = 200.
Finally, we take the square root of the variance to find the standard deviation:
√200 ≈ 14.1421.
However, since the options provided do not have this exact value, we can round it to the nearest half, which gives us 14 as the closest value (Option D).