5 A sample of 4 mothers was taken The mothers were asked the

5. A sample of 4 mothers was taken. The mothers were asked the age of their oldest child. You are given their responses below. 3 11 4 8 5a. Determine the mean.

Solution

5a. Average = (3+11+4+8)/ 4 = 6.5
5b.
b)
Step 1:Add them up:
3+11+4+8 = 26

Step 2: Square your answer:
26 × 26 = 676
…and divide by the number of items. We have 4 items in our example so:
676/ 4 = 169
Set this number aside for a moment.

Step 3: Take your set of original numbers from Step 1, and square them individually this time:
3^2+11^2+4^2+8^2= 210

Step 4: Subtract the amount in Step 2 from the amount in Step 3.
210 – 169 = 41
Set this number aside for a moment.

Step 5: Subtract 1 from the number of items in your data set. For our example:
4 – 1 = 3

Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance:
41/ 3 = 13.66
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:

13.66 = 3.696