Question

Gabriella asked 555 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, 114,8,8,9,114, comma, 8, comma, 8, comma, 9, comma, 11 The mean of these amounts is \bar x=8 x ˉ =8x, with, \bar, on top, equals, 8 gigabytes. What is the standard deviation? Round your answer to two decimal places. s_x\approxs x ​ ≈s, start subscript, x, end subscript, approximately equals gigabytes

Answer 1

Answer:

The standard deviation of the sample is 2.55 gigabytes

Step-by-step explanation:

Here we have the responses as follows;

Storage space usage on their computer $x_i$

The number of respondents or sample size, n = 5

        $x_i$            $(x_i - \bar x)$         $(x_i - \bar x)^{2}$

        4                -4                 16

        8                 0                  0

        8                 0                  0

        9                 1                   1

        11                 3                  9

∑      40                                   26

The sum = ∑X = 4 + 8 + 8 + 9 + 11 = 40

The mean  = (The sum)/(The count) = 40/5 = 8

Formula for population standard deviation is;

$\sigma = \sqrt{\frac{\Sigma (x_i - \mu)^2}{n } }$

Where:

σ = Population standard deviation

μ = Population mean

Since we are dealing with only 5 out of her hundreds of coworkers we are dealing with a sample therefore;

The formula for sample standard deviation is;

$s = \sqrt{\frac{\Sigma (x_i - \bar x)^2}{n - 1} }$

Where:

s = Sample standard deviation

n = Sample size

$x_i$ = Each value of the sample

$\bar x$ = Sample mean

We find each value of $(x_i - \bar x)$ by subtracting the x values from the mean, 8, as in the table above, next we find $(x_i - \bar x)^{2}$ by squaring the $(x_i - \bar x)$.

Next, we find the sum of the differences from the mean square values from the table after which we divide by n - 1, to get ${\frac{\Sigma (x_i - \bar x)^2}{n - 1} } = \frac{26}{5 - 1} = \frac{26}{4} = 6.5$

We find the root of the result which gives us the standard deviation hence

√6.5 = 2.5495.

Standard deviation, s = 2.5495 ≈ 2.55 to two significant places of decimal.