1. Compute arithmetic mean for the following data.
58, 62, 48, 53, 70, 52, 60, 84, 75
2. Compute the mean weight of a group of students of an university from the following data.
3. Find the arithmetic mean for the following distribution.
4. Two variables x and y are related by 2x + 3y + 7 = 0. If the arithmetic mean of x is 15, then find the arithmetic mean of y.
5. The mean salary for a group of 40 female workers is $5200 per month and that for a group of 60 male workers is $6800 per month. What is the combined mean salary?
1. Answer :
Formula to find geometric mean :
x̄ = ∑x/n
Fitting the given data in to the above formula, we get
x̄ = (58 + 62 + 48 + 53 + 70 + 52 + 60 + 84 + 75)/9
= 562/9
≈ 62.44
2. Answer :
Computation of mean weight of 36 students.
For to find arithmetic mean for the above data :
x̄ = ∑fx/N
N = ∑f = 36
∑fx = 2211
Mean weight :
x̄ = 2211/36
≈ 61.42 kg
3. Answer :
Computation of arithmetic mean :
Formula to find arithmetic mean for the above data :
x̄ = A + (∑fd/N) ⋅ C
A = Average of the largest and smallest mid-values
A = (479.5 + 359.5)/2 = 419.5
N = ∑f = 308
∑fd = - 43
C = 20
Arithmetic mean :
x̄ = 419.50 +(-43/308) ⋅ 20
= 419.50 - 860/308
≈ 416.71
4. Answer :
In 2x + 3y + 7 = 0, x and y are in linear relationship.
If two variables are in linear relationship, their arithmetic means also will be in the same linear relationship.
2x + 3y + 7 = 0
Solve for y.
3y = -2x - 7
y = (-2x - 7)/3
Arithmetic mean of y = (-7 - 2x̄)/3
Substitute x̄ = 15.
= (-7 - 2x15)/3
= (-7 - 30)/3
= -37/3
5. Answer :
Formula to find combined arithmetic mean :
x̄ = (n_{1}x̄_{1} + n_{2}x̄_{2})/(n_{1} + n_{2})
As given
n_{1} = 40, n_{2} = 60, x̄_{1} = 5200 and x̄_{2} = 6800
Combined mean salary :
x̄ = (40 ⋅ 5200 + 60 ⋅ 6800)/(40 + 60)
= (208000 + 408000)/100
= 616000/100
= $6160
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