Question

The mean of the following frequency distribution is 7.2 and the sum of all the frequencies is 40. Find the values of p and q.
Marks 5 6 7 8 9
No. of students 6 p 16 13 q



PLEASE HELP​

Answer 1

Answer:

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a = 1

b = 4

Step-by-step explanation:

GIVEN :-

MEAN = 7.2

$\sf{f_i\:total\:=\:40}$

TO FIND :-

The value of a & b.

SOLUTION :-

➝ N = 40

Mean = $\sf{\dfrac{Σf_ix_i}{N}}$

➝ 35 + a + b = 40

➝ a + b = 5. .,.,.,.,.,.,.,., (i)

➝ 7.2 = $\sf{\dfrac{246\:+\:6a\:9b}{40}}$

➝ 40 = 6a + 9b. .,.,.,.,.,.,. (ii)

By elimination method,

multiply equation(i) by 6 to eliminate a.

➝$\sf{\cancel{6a}\:+\:9b\:=\:42}$

➝$\sf{\cancel{6a}\:+\:6b\:=\:30}$

➝3b = 12

➝$\sf{b\:=\:\dfrac{12}{3}}$

➝$\sf\boxed{b = 4}$

putting value of b in equation (i)

➝a + b = 5

➝a + 4 = 5

➝a = 5 - 4

➝$\sf\boxed{a = 1}$

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