The mean of the following distribution is 50.
x f
10 17
30 5a + 3
50 32
70 7a - 11
90 19
Find the value of a and hence the frequencies of 30 and 70.
Solution:
Given, the mean of the following distribution is 50.
We have to find the value of a and the frequencies of 30 and 70.
We know that, Mean of ungrouped data = Mean = ∑fx / ∑f
Where, f are the frequencies of x
So, mean = [(17 × 10) + [(5a + 3) × 30] + (32 × 50) + [(7a - 11) × 70] + (19 × 90)] / (17 + 5a + 3 + 32 + 7a - 11 + 19)
50 = [170 + 150a + 90 + 1600 + 490a - 770 + 1710] / (12a + 60)
50 = (3570 - 770 + 640a)/(12a + 60)
50(12a + 60) = 2800 + 640a
600 a + 3000 = 2800 + 640a
640a - 600a = 3000 - 2800
40a = 200
a = 200/40
a = 20/4
a = 5
Therefore, the value of a is 5
Frequency of 30 = 5a + 3
= 5(5) + 3
= 25 + 3
= 28
Frequency of 70 = 7a - 11
= 7(5) - 11
= 35 -11
= 24
Therefore, the frequencies of 30 and 70 are 28 and 24.
✦ Try This: The mean of the following distribution is 50.
x | f |
10 | 15 |
30 | 6a + 6 |
50 | 45 |
70 | 2a + 11 |
90 | 21 |
Find the value of a and hence the frequencies of 30 and 70.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 14
NCERT Exemplar Class 9 Maths Exercise 14.4 Problem 10
The mean of the following distribution is 50. x f 10 17 30 5a + 3 50 32 70 7a - 11 90 19. Find the value of a and hence the frequencies of 30 and 70.
Summary:
The mean of the following distribution is 50. The value of a is 5 and hence the frequencies of 30 and 70 are 28 and 24 respectively
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