Question

gabriella asked 5 of her hundreds of coworkers how much storage space they were currently using on their computer. here are their responses (in gigabytes):
4, 8, 8, 9, 11
the mean of these amounts is (\bar{x} = 8) gigabytes.
what is the standard deviation?
round your answer to two decimal places.
(s_x approx square) gigabytes
show calculator

Explanation:

Step1: Find the squared differences from the mean

For each data point \( x \), calculate \( (x - \bar{x})^2 \). The mean \( \bar{x} = 8 \).

• For \( x = 4 \): \( (4 - 8)^2 = (-4)^2 = 16 \)
• For \( x = 8 \): \( (8 - 8)^2 = 0^2 = 0 \)
• For \( x = 8 \): \( (8 - 8)^2 = 0^2 = 0 \)
• For \( x = 9 \): \( (9 - 8)^2 = 1^2 = 1 \)
• For \( x = 11 \): \( (11 - 8)^2 = 3^2 = 9 \)

Step2: Calculate the sum of squared differences

Sum these squared differences: \( 16 + 0 + 0 + 1 + 9 = 26 \)

Step3: Divide by \( n - 1 \) (for sample standard deviation)

Here, \( n = 5 \), so \( n - 1 = 4 \). The variance \( s^2 = \frac{26}{4} = 6.5 \)

Step4: Take the square root of the variance

The standard deviation \( s_x = \sqrt{6.5} \approx 2.55 \)

Answer:

\( 2.55 \)