Question

Exercise 14.1

The number of movies attended in the preceding three months are given below for 30 people. Calculate the mean, the median, the mode, and the range. Show your work. Interpret each statistic.

0 15 26 8 2

3 11 13 0 3

0 1 17 1 9

7 4 18 12 10

   10 4 2 7 2

2 5 9 6 6

1. Calculate the mean and interpret the results.

2. Calculate the median and interpret the results.

3. Calculate the mode and interpret the results.

4. Compare the three measures of central tendency you have calculated in terms of the information provided.

5. Calculate the range and interpret the results.

Answer 1

1.

= (0+15+26+8+2+3+11+13+0+3+0+1+17+1+9+7+4+18+12+10+10+4+2+7+2+2+5+9+6+6)/2 = 7.1

Interpretation: On an average, people have watched 7 movies in the last month

2.

Median is the center value of the sample when the sample observations are arranged in ascending order.

However, since the number of samples is even (30), there are two central values.

So, the median is the average of these two values = (6+6)/2 = 6

Interpretation: Half of the people have watched more than 6 movies and the other half have watched less than 6 movies in the past month.

3.

'Mode' is the sample observation having the maximum frequency of occurrence.

Obs.	0	1	2	3	4	5	6	7	8	9	10	11	12	13	15	17	18	26	Total
Frequency	3	2	4	2	2	1	2	2	1	2	2	1	1	1	1	1	1	1	30

Note that the 2 times movie watching has the highest frequency count of 4. So, the mode is 2.

Interpretation: People who have watched exactly 2 movies are highest in number.

4.

The mean, median, and mode do not coincide in this particular case, which suggests that the data is off-centered or skewed. Since the mode and the median is shifted towards the left compared to the mean, we infer that the distribution is right-skewed. The following histogram also shows the same thing.

5.

So, Range = 26 - 0 = 26

The range is the measure of dispersion of the data. In this case, it is huge. Therefore, there is a large variation in movie-watching frequency among the people under study.