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 \(\rm \left(\frac{n+1}{2}\right)\) position.
- For even n, median is the mean of values at \(\rm \left(\frac{n}{2}\right)\) and \(\rm \left(\frac{n}{2}+1\right)\) 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 \(\rm \left(\frac{198}{2}\right)\) = 99th position and 99 + 1 = 100th position.
From the above table, both the 99th and 100th values are 3.
Therefore, the median of the above data is 3.
Last updated on May 30, 2025
->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.
-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.