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

Step2: Calculate the squared - differences

For 75: \((75 - 84)^2=(-9)^2 = 81\) (twice)
For 80: \((80 - 84)^2=(-4)^2 = 16\) (thrice)
For 85: \((85 - 84)^2=(1)^2 = 1\) (twice)
For 90: \((90 - 84)^2=(6)^2 = 36\) (twice)
For 100: \((100 - 84)^2=(16)^2 = 256\)
The sum of squared - differences is \(2\times81+3\times16 + 2\times1+2\times36+256=162 + 48+2+72+256=540\).

Step3: Calculate the variance

The variance \(s^{2}=\frac{\sum(x - \bar{x})^2}{n}=\frac{540}{10}=54\).

Step4: Calculate the standard deviation

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

Answer:

d. 7.3