Mean for Multiple-Observation Values

Suppose that a data set contains observation values occurring with frequencies,  respectively.

Example: A random sample of 50 personal property insurance policies showed the following number of claims over the past two years.      

No. of claims	No. of policies
0	21
1	13
2	5
3	4
4	2
5	3
6	2
Sum	50

Calculate the mean number of claims.

Solution:

Table 1:

No. of claims (mi)	No. of policies (fi)	fi*mi
0	21	0
1	13	13
2	5	10
3	4	12
4	2	8
5	3	15
6	2	12
Sum	50	70

Hence, mean number of claims= 

Problem: Calculate arithmetic mean of data of days to maturity 40 short-term investments.
Table 2: Data of days to maturity 40 short-term investments.

Class interval	No. of investments
30—39	3
40—49	1
50—59	8
60—69	10
70—79	7
80—89	7
90—99	4
Total	40

Solution:

Table 3: Calculation of arithmetic mean of data of days to maturity 40 short-term investments.

Class interval	Midpoint (mi)	Frequency (fi)	fi*mi
30—39	34.5	3	103.5
40—49	44.5	1	44.5
50—59	54.5	8	436
60—69	64.5	10	645
70—79	74.5	7	521.5
80—89	84.5	7	591.5
90—99	94.5	4	378
Total		40	2720