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Question
Find Q1, Q3, D8 and P67 of the following data:
| Size of Shares | 4 | 4.5 | 5 | 5.5 | 6 | 6.5 | 7 | 7.5 | 8 |
| Frequency | 10 | 18 | 22 | 25 | 40 | 15 | 10 | 8 | 7 |
Solution
| Size of Shares | Frequency | Cumulative Frequency |
| 4 | 10 | 10 |
| 4.5 | 18 | 28 |
| 5 | 22 | 50 |
| 5.5 | 25 | 75 |
| 6 | 40 | 115 |
| 6.5 | 15 | 130 |
| 7 | 10 | 140 |
| 7.5 | 8 | 148 |
| 8 | 7 | 155 |
| N = 155 |
Q1 = Size of `(("N" + 1)/4)^"th"` value
= Size of `((155 + 1)/4)^"th"` value
= Size of 39th value
Q1 = 5
Q3 = Size of `[3(("N" + 1)/4)]^"th"` value
= Size of `(3 xx 156/4)^"th"` value
= Size of 117th value
Q3 = 6.5
D8 = Size of `[8(("N" + 1)/10)]^"th"` value
= Size of `[8((155 + 1)/10)]^"th"` value
= Size of `(8 xx 156/10)^"th"` value
= Size of 124.8th value
D8 = 6.5
P67 = Size of `[67(("N" + 1)/100)]^"th"` value
= Size of `((67 xx 156)/100)^"th"` value
= Size of 104.52th value
P67 = 6
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