Using the data in the table, calculate the mean, range, variance, and standard deviation, and then answer questions e and f. Round the variance and standard deviation to one decimal place.

Question

a. Mean
b. Range
c. Variance
d. Standard deviation
e. What value is affecting the mean and SD of this distribution?
f. Does the mean adequately represent this distribution? If not, what would be a better measure of central tendency for this data set?
Pts LOS

1 1
2 3
3 5
4 3
5 2
6 29
7 3
8 4
9 2
10 1
11 2
Total 55

Answer 1

Find the mean first = sum of scores/number of scores.

Range = highest score - lowest score.

Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.

Standard deviation = square root of variance.

The mean acts like a fulcrum (balance point), therefore it is greatly modified by outlying scores (e.g., 29). If this is true, which of the remaining measures of central tendency would you use?

I'll let you do the calculations.