High School

The weights of seven boxes of cereal are: {12 oz, 10 oz, 8 oz, 9 oz, 10 oz, 13 oz, 15 oz}.

Compute the sample standard deviation.

A. 2.45 oz
B. 2.30 oz
C. 2.27 oz
D. 2.69 oz

Answer :

The sample standard deviation is a measure of the spread or variability of a set of data points in a sample. It quantifies how much the individual data points deviate from the mean of the sample. The correct option is 2.45 oz.

To compute the sample standard deviation for the given weights of the seven boxes of cereal, we can use the following steps:

Step 1: Calculate the mean (average) of the weights:

mean = (12 + 10 + 8 + 9 + 10 + 13 + 15) / 7 = 11 oz

Step 2: Calculate the difference between each weight and the mean:

deviations = [12 - 11, 10 - 11, 8 - 11, 9 - 11, 10 - 11, 13 - 11, 15 - 11]

= [1, -1, -3, -2, -1, 2, 4]

Step 3: Square each deviation:

squared_deviations = [1^2, (-1)^2, (-3)^2, (-2)^2, (-1)^2, 2^2, 4^2]

= [1, 1, 9, 4, 1, 4, 16]

Step 4: Calculate the sum of squared deviations:

sum_squared_deviations = 1 + 1 + 9 + 4 + 1 + 4 + 16 = 36

Step 5: Divide the sum of squared deviations by (n-1) to get the variance:

variance = sum_squared_deviations / (n-1) = 36 / (7-1) = 6

Step 6: Take the square root of the variance to get the sample standard deviation:

sample_std_deviation = sqrt(variance) = sqrt(6) ≈ 2.449

Therefore, the sample standard deviation of the given weights is approximately 2.449 oz Or approx 2.45 oz.

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