For the following data 10 21 23 27 34 35 37 41 46 68 81 x an

For the following data: 10, 21, 23, 27, 34, 35, 37, 41, 46, 68, 81

Solution

a

a)
Mean= 10 + 21 + 23 + 27 + 34 + 35 + 37 + 41 + 46 + 68 + 81/11=423/11=38.45

b)
Step 1:Add them up:
10 + 21 + 23 + 27 + 34 + 35 + 37 + 41 + 46 + 68 + 81 = 423

Step 2: Square your answer:
423 × 423 = 178929
…and divide by the number of items. We have 11 items in our example so:
178929 / 11 = 16266.27
Set this number aside for a moment.

Step 3: Take your set of original numbers from Step 1, and square them individually this time:
10^2+21^2+23^2+27^2+34^2+35^2+37^2+41^2+46^2+68^2+81^2 = 20531

Step 4: Subtract the amount in Step 2 from the amount in Step 3.
20531 – 16266.27 = 4264.73
Set this number aside for a moment.

Step 5: Subtract 1 from the number of items in your data set. For our example:
11 – 1 = 10

Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance:
4264.73/ 10 = 426.473
How to find the sample variance and standard deviation: Standard Deviation

Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation:

426.473 = 20.65