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Question
Answer the following questions on the basis of the given data :
| Marks | 10 | 20 | 30 | 40 | 50 |
| No. of Students | 4 | 7 | 13 | 8 | 6 |
1) Write the formula of Q1 and Q3.
2) Find out the median of the above data?
3) Find out the cumulative frequency of the last value in the above data.
4) Find out the value of 'n' in the above data
Solution
| Marks | No. of Students | cf |
| 10 | 4 | 4 |
| 20 | 7 | 11 |
| 30 | 13 | 24 |
| 40 | 8 | 32 |
| 50 | 6 | 38 |
| N = 38 |
1. Formula of Q1
Q1 = Size of 1`((n+1)/4)^"th" "observation"`
Formula of Q3
Q3 = Size of 3`((n+1)/4)^"th" "observation"`
2. Median = Q2
Median = Q2 = Size of 2`((n+1)/4)^"th" "observation"`
= Size of 2`((38+1)/4)^"th" "observation"`
= Size of 2`((39)/4)^"th" "observation"`
= Size of 2 (9.75)th observation
= Size of 19.5th observation
= Size of 19.5th observation lies in cf 24
Hence, quartile value = 30 marks.
3. The cumulative frequency of the last value in the above data is 38.
4. The value of 'n' in the above data is 38.
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