Question

the table below shows the scores on a math test. david 75 aaron 75 ashley 60 gina 75 andrew 75 kel 95 monica 100 anna 60 lucas 75 jennifer 65 find the standard deviation. round to the nearest tenth when necessary. a 157.25 c 9.1 b 12.5 d 12.3 please select the best answer from the choices provided

Explanation:

Step1: Calculate the mean

First, find the sum of all scores: \(75 + 60+75 + 100+75+75 + 95+60+65\)

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There are \(n = 10\) data points. The mean \(\bar{x}=\frac{755}{10}=75.5\)

Step2: Calculate the squared - differences from the mean

For each score \(x_i\), calculate \((x_i-\bar{x})^2\):

• For \(x = 75\): \((75 - 75.5)^2=(- 0.5)^2 = 0.25\) (occurs \(5\) times)
• For \(x = 60\): \((60 - 75.5)^2=(-15.5)^2=240.25\) (occurs \(2\) times)
• For \(x = 100\): \((100 - 75.5)^2=(24.5)^2 = 600.25\)
• For \(x = 95\): \((95 - 75.5)^2=(19.5)^2=380.25\)
• For \(x = 65\): \((65 - 75.5)^2=(-10.5)^2 = 110.25\)

The sum of squared - differences \(\sum_{i = 1}^{n}(x_i-\bar{x})^2=5\times0.25+2\times240.25 + 600.25+380.25+110.25\)

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Step3: Calculate the variance and standard deviation

The variance \(s^{2}=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n}=\frac{1572.5}{10}=157.25\)
The standard deviation \(s=\sqrt{157.25}\approx12.5\)

Answer:

b. 12.5