Question

the table below shows the scores on a science test. john 75 brett 80 elizabeth 90 cindy 100 jake 75 kenji 85 rick 80 joy 80 raul 90 suni 85 find the standard deviation. round to the nearest tenth when necessary. a. 53.3 c. 6 b. 8.2 d. 7.3

Explanation:

Step1: Calculate the mean

The scores are 75, 90, 75, 80, 90, 80, 100, 85, 80, 85.
The sum of scores is \(75 + 90+75 + 80+90+80+100+85+80+85=840\).
There are \(n = 10\) scores.
The mean \(\bar{x}=\frac{840}{10}=84\).

Step2: Calculate the squared - differences

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

Step3: Calculate the variance

The sum of squared - differences is \(81+36 + 81+16+36+16+256+1+16+1=540\).
The variance \(s^{2}=\frac{540}{10}=54\).

Step4: Calculate the standard deviation

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

Answer:

d. 7.3