Answer to Question #139722 in Statistics and Probability for Sohyun Ravena

Question

III. Create a grouped frequency distribution table for the statement below, the table must contain:
1. Class intervals
2. Frequency distribution and percentage
3. Cumulative frequency distribution and percentage
A Psychology 1100 class of BA Procrastination just got their final row score of the course:
49 68 36 52 65 95 97 91 35 56
34 58 42 91 54 59 34 70 93 33
58 32 67 89 81 67 93 43 46 88
50 63 54 68 59 36 66 50 41 78
62 39 82 77 31 35 41 86 52 31

Answer 1

Solution

Class Interval

The class intervals should accommodate all the values in the distribution.

We first determine the smallest and largest values i.e. 31 and 97 resp.

Obtaining the range (97-31=66) gives us an idea of widths of the class intervals. The total number of classes should lie between 6 and 12, therefore the appropriate class width that would ensure the number of classes are within the required range is 10.

Frequency distribution and Percentage

The frequency of a particular class is obtained by counting the number of scores that lie within its boundaries, e.g. there are 6 scores that lie between 40 and 49 (40 and 49 inclusive).

The percentage is obtained using the following formula:

$${frequency \over Total \space frequency}*100$$

Cumulative Frequency and Percentage

Cumulative frequency of a class is obtained by summing the frequency of that particular class with the frequencies of all other classes preceding it.

The percentage is similarly obtained as:

$${cumulative \space frequency \over Total \space cumulative \space frequency}*100$$