Arithmetic mean
Arithmetic means is commonly known as average or mean it is acquired by first of all summing up the values provided and by dividing the total value by the total no. of observations.
That is mean = ( ΣX)/n
Whereas x = no. of values
∑ = summation
n = no of observations
Illustration
The mean of 60, 80, 90, 120
(60 + 80 + 90 + 120)/4
= 350/4
= 87.5
The arithmetic mean is extremely useful since it represents the values of most observations in the population.
Therefore the mean describes the population rather well in terms of the magnitudes attained by most of the members of the population
Computation of the mean from grouped Data that is in classes.
The given data was acquired from the manufacturers of electronic cells. A sample of electronic cells was taking and the life spans were recorded as displayed in the given table:
Life span hrs

No. of cells (f)

Class MP(x)

X  A = d

fd

1600  1799

25

1699.5

600

15000

1800  1999

32

1899.5

400

12800

20002199

46

2099.5

200

9200

2200  2399

58

2299.5(A)

0

0

2400  2599

40

2499.5

200

8000

2600  2799

30

2699.5

400

12000

2800  2999

7

2899.5

600

4200

A = Assumed mean that this is an arbitrary number chosen from the data, MP = mid point
Arithmetic means = Assumed mean +(åfd)/(f)
2299.5 + (((12800)/238))
= 2299.5 +(53.78)
2245.72 hours
Illustration 2
Employ of the coded method The given data was acquired from students who were registered in a specific college.
The table displays the age distribution:
Age (yrs)

No. of Students (f)

mid points (x)

xa = d

D/c = u

fu

15  19

21

17

15

3

63

20  24

35

22

10

2

70

25  29

38

27

5

1

38

30  34

49

32(A)

0

0

0

35  39

31

37

+5

+

31

40  44

19

42

+10

+2

38


193




102

Required compute the mean age of the students by using the coded method
= 32 + ((102)/193) * 5
= 29.36 years