The monthly salary distribution of 250 families in a certain locality in agra is given below: monthly salary more than 0 more than 500 more than 1000 more than 1500 more than 2000 more than 2500 more than 3000 more than 3500 no. of families 250 200 120 80 55 30 15 5 find
a.limits of the income of middle 50% of the families
Answers
Step-by-step explanation:
a. firstly we have to convert the series
salary no. of students(f). c.f
0-500. 50. 50
500-1000. 80. 130
1000-1500. 40. 170
1500-2000. 25. 195
2000-2500. 25. 220
2500-3000. 15. 235
3000-3500. 10. 245
3500-4000 5. 250
we have to find the limits of middle 50% of the families
Q1 ------------- Q3
25%. 50% 75%
middle50% will have their income between Q3 and Q1
Q1 = N÷4 th item = 250÷ 4= 62.5 th item
it lies in the class interval 500-1000
62.5 -50
Q1 = 500 + ------------- ×. 500
80
Q1 = 500+ 78.125 = 578.125
Q3 = 3N ÷ 4 = 3(250) ÷ 4 = 187.5 th item
it lies in class interval 1500-2000
187.5-170
Q3 = 1500 + ------------ × 500
25
Q3 = 1500 + 350 = 1850
so ,
limits of middle 50% families = 578.125 - 1850