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Median When data are summarized in a frequency distribution, the median can be found by
Chapter 3, Problem 39(choose chapter or problem)
Median When data are summarized in a frequency distribution, the median can be found by first identifying the median class, which is the class that contains the median. We then assume that the values in that class are evenly distributed and we interpolate. Letting n denote the sum of all class frequencies, and letting m denote the sum of the class frequencies that precede the median class, the median can be estimated as shown here: ( lower limit of median class ) + ( class width ) ( ( n + 1 2 ) ( m + 1 ) frequency of median class ) Use this procedure to find the median of the frequency distribution given in Exercise 29. How does the result compare to the median found from the original list of data, which is 33.0 years? Which value of the median is better: the value computed using the frequency table or the value of 33.0 years?
Questions & Answers
QUESTION:
Median When data are summarized in a frequency distribution, the median can be found by first identifying the median class, which is the class that contains the median. We then assume that the values in that class are evenly distributed and we interpolate. Letting n denote the sum of all class frequencies, and letting m denote the sum of the class frequencies that precede the median class, the median can be estimated as shown here: ( lower limit of median class ) + ( class width ) ( ( n + 1 2 ) ( m + 1 ) frequency of median class ) Use this procedure to find the median of the frequency distribution given in Exercise 29. How does the result compare to the median found from the original list of data, which is 33.0 years? Which value of the median is better: the value computed using the frequency table or the value of 33.0 years?
ANSWER:Step 1 of 3
Given a frequency distribution table:
Age of Best Actress when Oscar was won |
Frequency |
20-29 |
27 |
30-39 |
34 |
40-49 |
13 |
50-59 |
2 |
60-69 |
4 |
70-79 |
1 |
80-89 |
1 |
Also, the median from the original list of data is 33.0.
First, we identify the median of the given data.
The sum of all frequencies in the given table is
Now, obtain 
Cumulative frequencies are shown below:
Class interval |
Frequency |
Cumulative frequency |
20-29 |
27 |
27 |
30-39 |
34 |
61 |
40-49 |
13 |
74 |
50-59 |
2 |
76 |
60-69 |
4 |
80 |
70-79 |
1 |
81 |
80-89 |
1 |
82 |
Total |
82 |