Question

Find the standard deviation of a series of ACT scores listed below.32, 20. 14, 16, 13The standard deviation is(Type an integer or decimal rounded to the nearest hundredth as needed.)

Answer 1

we have the data set

32, 20. 14, 16, 13

step 1

Find out the mean

mean=(32+20+14+16+13)/5

mean=95/5

mean=19

step 2

Find each score's deviation from the mean and square the result

(32-19)^2=169

(20-19)^2=1

(14-19)^2=25

(16-19)^2=9

(13-19)^2=36

step 3

Find the sum of squares

Sum=(169+1+25+9+36)

Sum=240

step 4

Divide the sum by the number of values in the data set (n)

n=5

so

Sum/n=240/5=48

step 5

To find out the standard deviation calculate the square root of 48

standard deviation=√48

standard deviation=6.9 -----> rounded to one decimal place