Question

Find the standard deviation of a series of ACT scores listed below.14, 16, 13, 31, 21The standard deviation is(Type an integer or decimal rounded to the nearest hundredth as needed.)

Answer 1

ANSWER

s = 7.38

EXPLANATION

The standard deviation, s, of a sample is the square root of the variance, s²,

$s^2=\frac{1}{n-1}\sum_{i\mathop{=}1}^n(x_i-\bar{x})^2$

Where n is the number of data, 5, and x with the line on top is the mean,

$\bar{x}=\frac{14+16+13+31+21}{5}=19$

So the variance is,

$s^2=\frac{1}{5-1}((14-19)^2+(16-19)^2+(13-19)^2+(31-19)^2+(21-19)^2)$

Solve the subtractions,

$s^2=\frac{1}{4}((-5)^2+(-3)^2+(-6)^2+(12)^2+(2)^2)$

Solve the squares, add and divide by 4,

$s^2=\frac{1}{4}(25+9+36+144+4)=\frac{218}{4}=54.5$

Finally, to find the standard deviation, take the square root,

$s=\sqrt{54.5}\approx7.38$

Hence, the standard deviation is 7.38, rounded to the nearest hundredth.