In a data distribution, the first quartile, the median and the means are 30.8, 48.5 and 42.0 respectively. If the coefficient skewness is −0.38 , use the information to answer questions 1 and 2
1. What is the approximate value of the third quartile, correct to 2 decimal places? Answer:
2. What is the approximate value of the variance, correct to the nearest whole number? Answer:
Answers
Step-by-step explanation:
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Given : In a data distribution, the first quartile, the median and the mean are 30.8, 48.5 and 42.0 respectively. the coefficient skewness is -0.38
To find : value for the third quartile?
Solution:
Q1 = 30.8
Median Q2 = 48.5
Mean = 42
Mean < median hence -ve coefficient skewness
coefficient skewness = (Q1 + Q3 - 2Q2)/(Q3 - Q1)
-0.38 = (30.8 + Q3 - 2(48.5) )/(Q3 - 30.8)
=> -0.38Q3 + 11.704 = 30.8 + Q3 - 97
=> 1.38Q3 = 77.904
=> Q3 = 56.45
value for the third quartile = 56.45
3IQR = 4SD
IQR = 56.45 - 30.8 = 25.65
SD = 3(25.65)/4 = 19.24
Variance = SD² = 370
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