Question

5. For each of the following, determine the interval width that would be best for a grouped frequency distribution and identify the approximate number of intervals needed to cover the range of series.

A. scores that range from X=6 to X= 81

B. Scores that range from X=18 to X=34

C. scores that range from X=56 to  X=97

Answer 1

Generally, we assume the number of intervals and then calculate the interval width from it, using the range of the observations

There are a few points which help in assuming the number of intervals:

1. Generally, we assume the number of intervals between 5 and 10

2. If the number of data points (n) is given then we assume the number of intervals (k) in such a way that

Here the number of data points is not given

A) Range = 81-6 = 75

Since the range is large we assume the number of intervals to be 10

Interval width = (Range)/(Number of intervals) = 75/10 =7.5

Therefore the interval width = 8 and number of intervals = 10

B) Range = 34-18 = 16

Since the range is small we assume the number of intervals to be 5

Interval width = (Range)/(Number of intervals) = 16/5 = 3.2

Therefore the interval width = 4 and number of intervals = 5

C) Range = 97-56 = 41

Since the range is large we assume the number of intervals to be 10

Interval width = (Range)/(Number of intervals) = 41/10 = 4.1

Therefore the interval width = 5 and number of intervals = 10