Question

A researcher records the following scores on a working memory quiz for two samples. Which sample has a larger standard deviation? Sample A: 2, 3, 4, 5, 6, 7, and 8 Sample B: 4, 5, 6, 7, 8, 9, and 10

Answer 1

Answer:

Standard deviations of both sets are equal

Step-by-step explanation:

We calculate the standard deviations for each sample set

For A

We calculate mean = (2+3+4+5+6+7+8)/7 = 35/5 = 7

We calculate deviations from the mean I.e each element in data set minus mean

x (x-mean)

2 -3

3. -2

4. -1

5. 0

6. 1

7 2

8. 3

If we look closely, we see that the sum of deviations is 0 , hence our standard deviation would be value zero too. This means there is no deviation about the mean

For the second set too, we calculate the mean = 4+5+6+7+8+9+10 = 49/7 = 7

We calculate the deviations too

X. X-mean

4. -3

5 -2

6 -1

7 0

8. 1

9 2

10. 3

Adding sum of deviations, we can see that the S.D is zero here too

Hence, the S.D of both data sets are equal