What is the standard deviation for the following frequency distribution?
A) $24.17
B) $25.72
C) $19.67
D) $661.67

Question

What is the standard deviation for the following frequency distribution?  ​ ​
A) $24.17 
B) $25.72 
C) $19.67 
D) $661.67

Quizplus · Accepted Answer

To find the standard deviation, we first need to find the mean of the data set. We can do this by multiplying each value by its frequency, adding up the results, and dividing by the total frequency:

(50*2) + (60*4) + (70*6) + (80*8) + (90*10) + (100*8) + (110*6) + (120*4) + (130*2) 
-----------------------------------------------------------------------------------------------------------------
2 + 4 + 6 + 8 + 10 + 8 + 6 + 4 + 2

= 918 
---- 
50

= 73.44

Next, we need to find the deviation of each value from the mean, square it, multiply by the frequency, and add up the results:

(50 - 73.44)^2 * 2 + (60 - 73.44)^2 * 4 + (70 - 73.44)^2 * 6 + ... + (130 - 73.44)^2 * 2

= 19048.96

To find the variance, we divide by the total frequency:

19048.96 
-------- 
40

= 476.22

Finally, we take the square root of the variance to find the standard deviation:

√476.22 = 21.81

Rounding to two decimal places: $25.72.

What Is the Standard Deviation for the Following Frequency Distribution