Question

1. A sample of n = 6 has a mean of M = 32. What is åX?

2. Find the mean for the following frequency distribution:

X	f
10	1
9	2
8	4
7	3
6	2

3. For the following scores, find the following:
   1. Mean
   2. Median
   3. Mode
   4. Based on the three values for central tendency, what is the most likely shape for this distribution of scores (symmetrical, positively skewed, or negatively skewed)?

26        40        21        17        48        31        37            22

24        13        30        28        29        19        44            34

35        20        7          42        39        31        40            11

4. What is the range for the set of scores in #3 above?

5. Given the following set of scores, find the variance and standard deviation: 5, 2, 8.

6. Calculate the following for this set of scores: 2, 10, 1, 3, 4.
   1. SS
   2. Variance and standard deviation, if this set of scores represents the entire population
   3. Variance and standard deviation, if this set of scores represents a sample of the entire population

7. Find the degrees of freedom (df) for the following samples:
   1. 15, 14, 9, 10, 11, 13
   2. 3, 5, 8, 14

Answer 1

(We solve these questions by using MS Excel. We input these data first and then use the various mathematical/statistical functions to calculate the values. We use the AVERAGE, MEDIAN, MODE, VAR, STDEV, SUM, VARP and STDEVP functions in MS Excel while calculating the values.)



6. (b) If entire population, then variance = 10, standard deviation = 3.1623.
(c) If sample of entire population, then variance = 12.5, standard deviation = 3.5355.

7. (a) degrees of freedom = n - 1 = 6 - 1 = 5.
(b) degrees of freedom = n - 1 = 4 - 1 = 3.
(Here, 'n' is the sample size.)