The ages of students in a class have been put into the frequency distribution below. What is the standard deviation for this (population)set of data?
A) 0.494
B) 0.703
C) 1.12
D) 1.25
E) 1.35

Question

The ages of students in a class have been put into the frequency distribution below.  What is the standard deviation for this (population)set of data?
A) 0.494 
B) 0.703 
C) 1.12 
D) 1.25 
E) 1.35

Quizplus · Accepted Answer

Using the frequency distribution, we can first find the mean:

mean = (5*13 + 9*14 + 10*15 + 6*16 + 5*17) / 35 = 15.14

Next, we can calculate the deviations from the mean for each age:

13 - 15.14 = -2.14
14 - 15.14 = -1.14
15 - 15.14 = -0.14
16 - 15.14 = 0.86
17 - 15.14 = 1.86

Using these deviations, we can calculate the variance:

variance = [(5*(-2.14)^2) + (9*(-1.14)^2) + (10*(-0.14)^2) + (6*(0.86)^2) + (5*(1.86)^2)] / 35 = 1.80

And finally, we can take the square root of the variance to get the standard deviation:

standard deviation = sqrt(1.80) = 0.703

Therefore, the answer is choice B.

The Ages of Students in a Class Have Been Put