Question

Gabriella asked

5
55 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
4,8,8,9,114, comma, 8, comma, 8, comma, 9, comma, 11
The mean of these amounts is
�
ˉ
=
8
x
ˉ
=8x, with, \bar, on top, equals, 8 gigabytes.
What is the standard deviation?
Round your answer to two decimal places.

Answer 1

To calculate the standard deviation for Gabriella's coworkers' storage space usage, you can follow these steps:

Step 1: Find the mean (average) of the data points.
Mean (\( \bar{x} \)) = (4 + 8 + 8 + 9 + 11) / 5 = 40 / 5 = 8 gigabytes.

Step 2: Find the squared difference between each data point and the mean.

For each data point:
- (4 - 8)^2 = 16
- (8 - 8)^2 = 0
- (8 - 8)^2 = 0
- (9 - 8)^2 = 1
- (11 - 8)^2 = 9

Step 3: Calculate the variance, which is the average of these squared differences.

Variance (\( \sigma^2 \)) = [(16 + 0 + 0 + 1 + 9) / 5] = 26 / 5 = 5.2 square gigabytes.

Step 4: Find the standard deviation, which is the square root of the variance.

Standard Deviation (\( \sigma \)) ≈ √5.2 ≈ 2.28 (rounded to two decimal places) gigabytes.

So, the standard deviation of their storage space usage is approximately 2.28 gigabytes.