Question

the table below shows the scores on a science test.

find the standard deviation. round to the nearest tenth when necessary.
a. 53.3
c. 6
b. 8.2
d. 7.3

please select the best answer from the choices provided

Explanation:

Step1: Calculate the mean

The data set is \(75,80,90,100,75,85,80,80,90,85\).
The mean \(\bar{x}=\frac{75 + 80+90+100+75+85+80+80+90+85}{10}=\frac{840}{10} = 84\)

Step2: Calculate the squared differences from the mean

\((75 - 84)^2=(-9)^2 = 81\), \((80 - 84)^2=(-4)^2=16\), \((90 - 84)^2=(6)^2 = 36\), \((100 - 84)^2=(16)^2=256\), \((75 - 84)^2=81\), \((85 - 84)^2=(1)^2 = 1\), \((80 - 84)^2=16\), \((80 - 84)^2=16\), \((90 - 84)^2=36\), \((85 - 84)^2=1\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{81+16+36+256+81+1+16+16+36+1}{10}=\frac{540}{10}=54\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{54}\approx7.3\)

Answer:

d. \(7.3\)