Advertisements
Advertisements
Question
Find lower quartile, upper quartile, 7th decile, 5th decile and 60th percentile for the following frequency distribution.
| Wages | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |
| Frequency | 1 | 3 | 11 | 21 | 43 | 32 | 9 |
Advertisements
Solution
| Wages | Frequency | Cumulative Frequency |
| 10 - 20 | 1 | 1 |
| 20 - 30 | 3 | 4 |
| 30 - 40 | 11 | 15 |
| 40 - 50 | 21 | 36 |
| 50 - 60 | 43 | 79 |
| 60 - 70 | 32 | 111 |
| 70 - 80 | 9 | 120 |
| N = 120 |
Lower quartile, Q1 = size of `("N"/4)^"th"` value
= size of `(120/4)^"th"` value
= size of 30th value
Q1 lies in the class (40 - 50) and its corresponding values are L = 40, `"N"/4` = 30, pcf = 15, f = 21 and C = 10
Q1 = `"L" +[("N"/4 - "pcf")/"f"] xx "C"`
= `40 + ((30 - 15)/21) xx 10`
= `40 + 15/21 xx 10`
= 40 + 7.14
= 47.4
Q3 = size of `("3N"/4)^"th"` value
= size of `((3 xx 120)/4)^"th"` value
= size of 90th value
Q3 lies in the class (60 - 70) and its corresponding values are L = 60, `"3N"/4` = 90, pcf = 79, f = 32 and C = 10.
Q3 = `"L" +[("3N"/4 - "pcf")/"f"] xx "C"`
= `60 + ((90 - 79)/32) xx 10`
= `60 + 11/32 xx 10`
= 60 + 3.4375
= 63.4375
= 63.44
7th decile = D7 = size of `("7N"/10)^"th"` value
= size of `((7 xx 120)/10)^"th"` value
= size of 84th value
Thus D7 lies in the class (60 - 70) and its corresponding values are L = 60, `"7N"/10` = 84, pcf = 79, f = 32 and C = 10.
D7 = `"L" +[("7N"/10 - "pcf")/"f"] xx "C"`
= `60 + ((84 - 79)/32) xx 10`
= `60 + 5/32 xx 10`
= `60 + 50/32`
= 60 + 1.5625
= 60 + 1.56
= 61.56
5th decile = D5 = size of `("5N"/10)^"th"` value
= size of `((5 xx 120)/10)^"th"` value
= size of 60th value
Thus D5 lies in the class (50 - 60) and its corresponding values are L = 50, `"5N"/10` = 60, pcf = 36, f = 43 and C = 10.
D5 = `"L" +[("5N"/10 - "pcf")/"f"] xx "C"`
= `50 + ((60 - 36)/43) xx 10`
= `50 + 24/43 xx 10`
= `50 + 240/43`
= 50 + 5.581
= 55.581
= 55.58
P60 = size of `("60N"/100)^"th"` value
= size of `((60 xx 120)/100)^"th"` value
= size of 72th value
Thus P60 lies in the class (50 - 60) and its corresponding values are L = 50, `"60N"/100` = 72, pcf = 36, f = 43 and C = 10.
P60 = `"L" +[("60N"/100 - "pcf")/"f"] xx "C"`
= `50 + ((72 - 36)/43) xx 10`
= `50 + 36/43 xx 10`
= 50 + 8.37
= 58.37
APPEARS IN
RELATED QUESTIONS
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 |
An aeroplane flies, along the four sides of a square at speeds of 100, 200, 300 and 400 kilometres per hour respectively. What is the average speed of the plane in its flight around the square?
Calculate AM, GM and HM from the following data and also find its relationship:
| Marks: | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 |
| No. of students: | 5 | 10 | 25 | 30 | 20 | 10 |
The harmonic mean of the numbers 2, 3, 4 is:
The geometric mean of two numbers 8 and 18 shall be
If the mean of 1, 2, 3, …, n is `(6"n")/11`, then the value of n is
The measure of central tendency that does not get affected by extreme values:
Answer the following question in about 30 words:
What are the advantages of using mode?
Which of the following best describes a 'measure of central tendency'?
If each value in a dataset is increased by the same constant, what happens to the mean and median?
