Advertisements
Advertisements
Question
For a distribution, Bowley’s coefficient of skewness is 0.6. The sum of upper and lower quartiles is 100 and median is 38. Find the upper and lower quartiles.
Solution
Given, Skb = 0.6, Q3 + Q1 = 100,
Median = Q2 = 38
Skb = `("Q"_3 + "Q"_1 - 2"Q"_2)/("Q"_3 - "Q"_1)`
∴ 0.6 = `(100 - 2(38))/("Q"_3 - "Q"_1)`
∴ 0.6(Q3 – Q1) = 100 – 76 = 24
∴ Q3 – Q1 = `24/0.6`
∴ Q3 – Q1 = 40 ....(i)
Q3 + Q1 = 100 ....(ii) (given)
Adding (i) and (ii), we get
2Q3 = 140
∴ Q3 = `140/2` = 70
Substituting the value of Q3 in (ii), we get
70 + Q1 = 100
∴ Q1 = 100 – 70 = 30
∴ upper quartile = 70 and lower quartile = 30.
APPEARS IN
RELATED QUESTIONS
For a data set, sum of upper and lower quartiles is 100, difference between upper and lower quartiles is 40 and median is 50. Find the coefficient of skewness.
For a data set with upper quartile equal to 55 and median equal to 42. If the distribution is symmetric, find the value of lower quartile.
Obtain the coefficient of skewness by formula and comment on nature of the distribution.
| Height in inches | No. of females |
| Less than 60 | 10 |
| 60 – 64 | 20 |
| 64 – 68 | 40 |
| 68 – 72 | 10 |
| 72 – 76 | 2 |
Calculate Skb for the following set of observations of yield of wheat in kg from 13 plots:
4.6, 3.5, 4.8, 5.1, 4.7, 5.5, 4.7, 3.6, 3.5, 4.2, 3.5, 3.6, 5.2
For a frequency distribution Q3 – Q2 = 90 And Q2 – Q1 = 120, find Skb.
For a distribution, Q1 = 25, Q2 = 35 and Q3 = 50. Find Bowley’s coefficient of skewness Skb.
For a distribution Q3 – Q2 = 40, Q2 – Q1 = 60. Find Bowley’s coefficient of skewness Skb.
Calculate Bowley’s coefficient of skewness Skb from the following data:
| Marks above | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
| No. of students | 120 | 115 | 108 | 98 | 85 | 60 | 18 | 5 | 0 |
Find Skb for the following set of observations:
18, 27, 10, 25, 31, 13, 28.
