Question

The graph below displays how many pieces of candy Timmy and his five friends each received last Halloween. Within how many standard deviations of the mean do the values fall?

A. 2
B. 1
C. 3
D. 4

Answer 1

So the values are 16,19, 25, 32, 38, 40. I used an online standard deviation calculator and the value you look at is the Standard Error of the mean. In the screenshot provided it shows that the answer is 4. Sorry I couldn't be of more help and give you instructions on how to solve this without a calculator. I haven't done that math in a while.

Answer 2

1) Calculate the mean:

mean = sum of the values / number of data = [16 + 19 + 25 + 32 + 38 + 40] / 6 = 28.33

3) Calculate the standard deviation:

Standard deviation^2 = { sum of (value - mean)^2 } / (number of data - 1) =

{ (16 - 28.33)^2 + (19 - 28.33)^2 + (25 - 28.33)^2 + (32 - 28.33)^2 + (38 - 28.33)^2 + (38 - 28.33)^2 + (40 - 28.33)^2 } / 6 = 493.33 / (6 - 1) = 98.66

=> standard deviation = √98.66 = 9.93

4) Maximum value - mean = 40 - 28.33 = 11.67

=> 11.67 / 9.93 = 1.17 times the standard deviation

Minimum value - mean = 16 - 28.33 = -12.33

-12.33 / 9.93 = - 1.24

5) Conclusion: all the values fall within 2 standard deviations of the mean.