Consider G. Thumb, the leading salesperson for the Moe D. Lawn Landscaping Company. Thumb turned in the following summary of clients contacted for the week of October 23–28.
Date No. of Clients
Oct. 23 11
Oct. 24 8
Oct. 25 11
Oct. 26 15
Oct. 27 11
Oct. 28 16
Find the standard deviation (rounded to the nearest hundredth).
Use same process described in my response to your previous post.
To find the standard deviation, follow these steps:
1. Calculate the mean (average) of the sample. In this case, add up the number of clients for each day and divide by the total number of days (6):
Mean = (11 + 8 + 11 + 15 + 11 + 16) / 6 = 72 / 6 = 12
2. Calculate the difference between each value and the mean. In this case, subtract the mean from each number of clients:
Oct. 23: 11 - 12 = -1
Oct. 24: 8 - 12 = -4
Oct. 25: 11 - 12 = -1
Oct. 26: 15 - 12 = 3
Oct. 27: 11 - 12 = -1
Oct. 28: 16 - 12 = 4
3. Square the differences obtained in step 2. This ensures that all values are positive:
(-1)^2 = 1
(-4)^2 = 16
(-1)^2 = 1
(3)^2 = 9
(-1)^2 = 1
(4)^2 = 16
4. Calculate the mean of the squared differences found in step 3. Add up the squared differences and divide by the total number of values:
Mean of squared differences = (1 + 16 + 1 + 9 + 1 + 16) / 6 = 44 / 6 ≈ 7.33
5. Calculate the square root of the mean of squared differences. This is the standard deviation:
Standard Deviation = √7.33 ≈ 2.71
Therefore, the standard deviation of the number of clients contacted for the week of October 23–28 is approximately 2.71.