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Question
Calculate all the quartiles for the following frequency distribution:
| No. of E-transactions per day | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| No. of days | 10 | 35 | 45 | 95 | 64 | 32 | 10 | 9 |
Solution
We construct the less than cumulative frequency table as given below:
| No. of E-transaction per day | No. of days | Less than cumulative frequency (c.f.) |
| 0 | 10 | 10 |
| 1 | 35 | 45 |
| 2 | 45 | 90 ← Q1 |
| 3 | 95 | 185 ← Q2 |
| 4 | 64 | 249 ← Q3 |
| 5 | 32 | 281 |
| 6 | 10 | 291 |
| 7 | 9 | 300 |
| Total | 300 |
Here, n = 300
Q1 = value of `(("n" + 1)/4)^"th"`observation
= value of `((300 + 1)/4)^"th"`observation
= value of (75.25)th observation
Cumulative frequency which is just greater than (or equal to) 75.25 is 90.
∴ Q1 = 2
Q2 = value of 2`(("n" + 1)/4)^"th"`observation
= value of 2`((300 + 1)/4)^"th"`observation
= value of (2 × 75.25)th observation
= value of (150.50)th observation
Cumulative frequency which is just greater than (or equal to) 150.50 is 185.
∴ Q2 = 3
Q3 = value of 3`(("n" + 1)/4)^"th"` observation
= value of 3`((300 + 1)/4)^"th"` observation
= value of (3 × 75.25)th observation
= value of (225.75)th observation
Cumulative frequency which is just greater than (or equal to) 225.75 is 249.
∴ Q3 = 4
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