# ARITHMETIC MEAN WORKSHEET

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?

Formula to find geometric mean :

∑x/n

Fitting the given data in to the above formula, we get

= (58 + 62 + 48 + 53 + 70 + 52 + 60 + 84 + 75)/9

= 562/9

62.44

Computation of mean weight of 36 students.

For to find arithmetic mean for the above data :

= ∑fx/N

N = ∑f = 36

∑fx = 2211

Mean weight :

= 2211/36

≈ 61.42 kg

Computation of arithmetic mean :

Formula to find arithmetic mean for the above data :

= 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 :

= 419.50 +(-43/308)  20

419.50 - 860/308

416.71

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 - 2)/3

Substitute  = 15.

= (-7 - 2x15)/3

= (-7 - 30)/3

= -37/3

Formula to find combined arithmetic mean :

= (n11 + n22)/(n1 + n2)

As given

n1 = 40, n2 = 60, 1 = 5200 and 2 = 6800

Combined mean salary :

= (40 ⋅ 5200 + 60 ⋅ 6800)/(40 + 60)

= (208000 + 408000)/100

= 616000/100

= \$6160

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