Question
Download Solution PDFThe following tables gives the frequency distribution of number of peas per pea pod of 198 pods:
|
Number of peas |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
Frequency |
4 |
33 |
76 |
50 |
26 |
8 |
1 |
What is the median of this distribution?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Median of 'n' observations is the value at the central position when the data is arranged in ascending or descending order.
- For, odd n, median is the value at the
position. - For even n, median is the mean of values at
and position.
Calculation:
Writing the cumulative frequencies, we get
|
Number of peas |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
Frequency |
4 |
33 |
76 |
50 |
26 |
8 |
1 |
| Cumulative Frequency | 4 | 37 | 113 | 163 | 189 | 197 | 198 |
Since n = 198 is even, the median will be the mean of the values at
From the above table, both the 99th and 100th values are 3.
Therefore, the median of the above data is 3.
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