The mean of the following distribution is 24. find the value of p Marks 0-10 10-20 20-30 30-40 40-50 50-60
no. of
students. 15. 20. 35. p. 10. 42

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-98.36

Explanation:

Given the data :

Marks 0-10 10-20 20-30 30-40 40-50 50-60

no.of students : 15. 20. 35. p. 10. 42

The given mean = 24

This is a grouped data:

The formula for the mean is :

Σfx / Σf

Where, x = midpoint ; f = frequency

The midpoint, x = (upper - lower limit) / 2

Midpoint of marks, x :

Marks x Frequency

0 - 10 5 15

10 - 20 15 20

20 - 30 25 35

30 - 40 35 p

40 - 50 45 10

50 - 60 55 42

[(5*15) + (15*20) + (25*35) + (35*p) + (45*10) + (55*42)] / (15+20+35+p+10+42) = 24

(75+300+875+35p+450+2310) / (122 + p) = 24

(4010 + 35p) / (122 + p) = 24

4010 + 35p = 24(122+p)

4010 + 35p = 2928 + 24p

4010 - 2928 = 24p - 35p

1082 = - 11p

p = 1082 / - 11

p = - 98.36

Kindly check the distribution given again as obtaining a negative value isn't ideal.