Question

Use the SAMPLE-level data set to answer the questions:

12 6 9 10 4 5 11 8 7 4

a. Compute SS for this data set

b. Compute s2 for this data set

c. Compute s for this data set

d. What is the definition for standard deviation?

Answer 1

given data set,

12, 6 ,9 ,10, 4 ,5, 11, 8 ,7, 4 sample data set

Mean = Sum of observations/ Count of observations
Mean = (12 + 6 + 9 + 10 + 4 + 5 + 11 + 8 + 7 + 4 / 10) = 7.6
computational formula SS = ΣX2 - ((ΣX)2 / N)
Variance
Step 1: Add them up
12 + 6 + 9 + 10 + 4 + 5 + 11 + 8 + 7 + 4 = 76
Step 2: Square your answer
76*76 =5776
…and divide by the number of items. We have 10 items , 5776/10 = 577.6
Set this number aside for a moment.
Step 3: Take your set of original numbers from Step 1, and square them individually this time
12^2 + 6^2 + 9^2 + 10^2 + 4^2 + 5^2 + 11^2 + 8^2 + 7^2 + 4^2 = 652
Step 4: Subtract the amount in Step 2 from the amount in Step 3
652 - 577.6 = 74.4
sum of squares of data (SS) = 74.4
Step 5: Subtract 1 from the number of items in your data set, 10 - 1 = 9
Step 6: Divide the number in Step 4 by the number in Step 5. This gives you the variance
74.4 / 9 = 8.2667
Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation
2.8752
Answers:
a.
sum of squares = ss= 74.4
b.
variance = sum of squares/n-1 = 74.4/9 = 8.226
c.
standard deviation = sqrt(variance) = 2.8752
d.
definition of standard deviation:
a statistic that measures the dispersion of a data set relative to its mean and also calculated as the square root of the variance.
If the data points are further from the mean, there is a higher deviation within the data set.
the more spread out the data, the higher the standard deviation