Practice Questions on Mean for Ungrouped Data :
Here we are going to see some practice questions on mean for ungrouped data.
Question 1 :
If the mean of the following data is 20.2, then find the value of p
x 10 15 20 25 30 |
f 6 8 p 10 6 --- 30 + p |
fx 60 120 20p 250 180 ------- 610 + 20p |
Mean = (610 + 20p)/(30 + p)
Mean = 20.2
(610 + 20p)/(30+p) = 20.2
610 + 20p = 20.2(30+p)
610 + 20 p = 606 + 20.2p
20.2p-20p = 610 - 606
0.2p = 4
p = 4/0.2
p = 20
Question 2 :
In the class, weight of students is measured for the class records. Calculate mean weight of the class students using Direct method.
Solution :
Weight 15-25 25-35 35-45 45-55 55-65 65-75 |
Mid value(x) 20 30 40 50 60 70 |
f 4 11 19 14 0 2 |
fx 80 330 760 700 0 140 ----- 2010 |
Mean = 2010 / 6
= 335
Question 3 :
Calculate the mean of the following distribution using Assumed Mean Method:
Solution :
A = 25
Weight 0-10 10-20 20-30 30-40 40-50 |
Mid value(x) 5 15 25 35 45 |
f 5 7 15 28 8 -- 63 |
d = x - 25 -20 -10 0 10 20 |
fd -100 -70 0 280 160 ------- 270 |
Mean = A + ∑ fd/∑ f
= 25 + (270/63)
= 25 + 4.28
Mean = 29.28
Question 4 :
Find the Arithmetic Mean of the following data using Step Deviation Method:
Solution :
Weight 14.5-19.5 19.5-24.5 24.5-29.5 29.5-34.5 34.5-39.5 39.5-44.5 |
x 17 22 27 32 37 42 |
f 4 20 38 24 10 9 -- 105 |
d=(x-32)/5 -15 => -3 -10 => -2 -5 => -1 0 => 0 5 => 1 10 => 2 |
fd -12 -40 -38 0 10 18 ------- -62 |
Mean = A + (∑ fd/∑f) x c
= 32 + (-62/105) x 5
= 32 - 0.59 (5)
= 32 - 2.95
Mean = 29.05
After having gone through the stuff given above, we hope that the students would have understood, "Finding Mean for Grouped Data Examples"
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