is this right?
Find the standard deviation to the given data. The manager of a small dry cleaner employs six people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. THe six distances are listed:
17.5,12.5,26.0,32.2,17.7,20.1. Round the result to two decimal places.
so the mean that i got was 21
then I found the square of the number within the list and added the results then i used the formula to find variance.
= (2892.64- 6 (21)^2)/ (6-1)
= i am ended up after calculations with
49.328
then i find the deviation squaring the answer.
sqrt 49.328 approx.= 7.023 and rounding to the two decimal places would be: 7.03 that would be my standard deviation
You found the sample n-1 deviation correctly, however, how did you round a 3 up?
to round up a 3 it should be next to it a 5 or above so...
7.023 rounded to two decimal places would look like 702.3 which would be 702.0 then or am i still wrong...
It seems there might be some confusion in your calculation and rounding process. Let's go through the steps again to find the correct standard deviation.
Step 1: Calculate the mean
To find the mean, add up all the distances and divide by the number of data points (in this case, 6):
Mean = (17.5 + 12.5 + 26.0 + 32.2 + 17.7 + 20.1) / 6 = 21.5 (rounded to one decimal place)
Step 2: Find the deviation for each data point
To find the deviation for each data point, subtract the mean from each distance:
Deviation for 17.5 = 17.5 - 21.5 = -4.0
Deviation for 12.5 = 12.5 - 21.5 = -9.0
Deviation for 26.0 = 26.0 - 21.5 = 4.5
Deviation for 32.2 = 32.2 - 21.5 = 10.7
Deviation for 17.7 = 17.7 - 21.5 = -3.8
Deviation for 20.1 = 20.1 - 21.5 = -1.4
Step 3: Find the variance
To find the variance, square each deviation and calculate their sum:
Variance = [(-4.0)^2 + (-9.0)^2 + (4.5)^2 + (10.7)^2 + (-3.8)^2 + (-1.4)^2] / (6-1) = 79.70 (rounded to two decimal places)
Step 4: Find the standard deviation
Finally, to find the standard deviation, take the square root of the variance:
Standard deviation = sqrt(79.70) ≈ 8.93 (rounded to two decimal places)
So the correct standard deviation for the given data is approximately 8.93.