Question

The graph represents the distribution of the number of questions answered correctly on a 50-question math test. A graph shows the horizontal axis numbered 24 to x. The vertical axis is unnumbered. The graph shows an upward trend from 24 to 36 then a downward trend from 36 to 48. What is the standard deviation of the data?

a)4

b)8

c)12

d)24

Answer 1

The standard deviation for this normal distribution is A. 4.

Explanation:

1. Let's review the information provided to answer the question correctly:

x-axis goes from 24 to x

y-axis unnumbered

Upward trend from 24 to 36

Downward trend from 36 to 48

2. What is the standard deviation of the data?

Let's recall that for the normal distribution, as we can see in the graph attached, the values start the upward trend when the x-axis is at the value of the mean minus 3 times the standard deviation and the downward trend finish when the x-axis is at the value of the mean plus 3 times the standard deviation and it accounts for 99.73% of the set, the sample or the population.

Therefore, for this case:

Mean = 36

Mean - 3 times the standard deviation = 24

Mean + 3 times the standard deviation = 48

Standard deviation = (36 - 24)/3 = 12/3 = 4

The standard deviation for this normal distribution is A. 4.

Moderator: Please don't delete the answer because of the graph attached. It's being used for educational purposes and as you can see, it's not advertising any website or company. Thanks in advance!