Question

suppose that every student in your class scored 75% on their first test. find the standard deviation of the exam scores. 0 1 0.75 0.87

Explanation:

Step1: Recall the formula for standard deviation

The formula for the standard deviation of a data - set \(x_1,x_2,\cdots,x_n\) is \(\sigma=\sqrt{\frac{1}{n}\sum_{i = 1}^{n}(x_i-\mu)^2}\), where \(\mu\) is the mean of the data - set.

Step2: Calculate the mean

Given that \(x_1=x_2=\cdots=x_n = 75\), the mean \(\mu=\frac{\sum_{i=1}^{n}x_i}{n}=\frac{75 + 75+\cdots+75}{n}=75\) (since there are \(n\) terms of \(75\)).

Step3: Calculate \((x_i-\mu)^2\)

Substitute \(x_i = 75\) and \(\mu = 75\) into \((x_i-\mu)^2\). We get \((75 - 75)^2=0\) for all \(i = 1,2,\cdots,n\).

Step4: Calculate the standard deviation

\(\sigma=\sqrt{\frac{1}{n}\sum_{i = 1}^{n}(x_i-\mu)^2}=\sqrt{\frac{1}{n}(0 + 0+\cdots+0)}=\sqrt{0}=0\)

Answer:

0