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प्रश्न
A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and the following data was obtained:
| Height in cm | Number of Girls |
| Less than 140 | 4 |
| Less than 145 | 11 |
| Less than 150 | 29 |
| Less than 155 | 40 |
| Less than 160 | 46 |
| Less than 165 | 51 |
Find the median height.
उत्तर
To calculate the median height, we need to find the class intervals and their corresponding frequencies
The given distribution being of thee less than type 140, 145, 150,…..,165 give the upper limits of the corresponding class intervals. So, the classes should be below 140, 145, 150,......, 160, 165 observe that from the given distribution, we find that there are 4-girls with height less than 140 is 4. Now there are 4 girls with heights less than 140. Therefore, the number of girls with height in the interval 140, 145 is 11- 4=7, similarly. The frequencies of 145 150 is 29-11=18, for 150-155 it is 40-29=11, and so on so our
frequencies distribution becomes.
| Class interval | Frequency | Cumulative frequency |
| below 140 | 4 | 4 |
| 140-145 | 7 | 11 |
| 145-150 | 18 | 29 |
| 150-155 | 11 | 40 |
| 155-160 | 6 | 46 |
| 160-165 | 5 | 51 |
Now N = 51
So, N/2=51/2=25.5
Now, the cumulative frequency just greater than 25.5 is 29 and the corresponding class is 145 - 150.
Therefore, 145 - 150 is the median class.
l = 145, f = 18, F = 11 and h = 5
We know that
Median `=l+(N/2-F)/fxxh`
`=145+(25.5-11)/18xx5`
`=145+14.5/18xx5`
`=145+72.5/18`
= 145 + 4.03
= 149.03
Hence, the median height is 149.03
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संबंधित प्रश्न
Compute the median for the following data:
| Marks | No. of students |
| More than 150 | 0 |
| More than 140 | 12 |
| More than 130 | 27 |
| More than 120 | 60 |
| More than 110 | 105 |
| More than 100 | 124 |
| More than 90 | 141 |
| More than 80 | 150 |
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