Question

standard deviation : tells you how far each score is from the mean. \high\ standard deviation is when the values are far from the mean. \low\ standard deviation is when values are clustered close to the mean. find the standard deviation for this data set. σ = √(σ(xᵢ - μ)² / n) σ = population standard deviation n = the size of the population xᵢ = each value from the population μ = the population mean example #6: a) median: b) mode: c) range: d) mean: e) standard deviation: employees in industry (in thousands) the number of employees in each industry in seattle was recorded and rounded to the nearest 10 thousand. the results are displayed in the dot - plot above. according to the dot plot, what is

Explanation:

Step1: Count data - points

There are 1 + 5+ 2+ 1+ 2+ 1+ 1 = 13 data - points.

Step2: List data values

The data values are: 0, 10, 10, 10, 10, 10, 20, 20, 30, 40, 70, 80, 90.

Step3: Calculate the mean $\mu$

$\mu=\frac{0 + 5\times10+2\times20 + 30+40+70+80+90}{13}=\frac{0 + 50+40 + 30+40+70+80+90}{13}=\frac{400}{13}\approx30.77$

Step4: Calculate $(x_i-\mu)^2$ for each $x_i$

For $x_1 = 0$: $(0 - 30.77)^2=946.79$
For $x_2 = 10$: $(10 - 30.77)^2 = 431.30$ (and do this for all 5 values of 10)
For $x_7 = 20$: $(20 - 30.77)^2 = 116.00$ (and do this for both 20s)
For $x_9 = 30$: $(30 - 30.77)^2 = 0.59$
For $x_{10}=40$: $(40 - 30.77)^2 = 85.27$
For $x_{11}=70$: $(70 - 30.77)^2 = 1539.09$
For $x_{12}=80$: $(80 - 30.77)^2 = 2423.61$
For $x_{13}=90$: $(90 - 30.77)^2 = 3508.27$

Step5: Calculate $\sum(x_i - \mu)^2$

Sum up all the $(x_i-\mu)^2$ values: $946.79+5\times431.30 + 2\times116.00+0.59+85.27+1539.09+2423.61+3508.27=946.79 + 2156.5+232+0.59+85.27+1539.09+2423.61+3508.27 = 10892.12$

Step6: Calculate the standard deviation $\sigma$

$\sigma=\sqrt{\frac{\sum(x_i - \mu)^2}{N}}=\sqrt{\frac{10892.12}{13}}\approx\sqrt{837.86}\approx28.94$

Answer:

Approximately 28.94