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### Middle/High School Algebra, Geometry, and Statistics (AGS)9.20 Arithmetic Mean of Discrete Values

Arithmetic Mean (A.M.)
Arithmetic Mean better known as average is the most commonly used measure of central tendency.

The mean of the n observations x1,x2,x3,x4........,xn is x where
x = x1,x2,x3,x4........,xn/n
Using the summation notation, the arithmetic mean of n observations x1,x2,x3,x4........,xn can be more simply expressed as

where x = Aritmetic mean
n = Number of observations
xi = ith observation of the variable x

= summation of all xi values

Example
• Find the mean of the following distribution :
 xi 12 13 14 15 16 17 18 fi 1 3 4 8 10 3 1
• Solution

Q 1: Five coins were simultaneously tossed 1000 times and at each toss the number of heads was observed. The number of tosses during which 0,1,2,3,4,5 heads were obtained are shown in the table below. Find the mean number of heads per toss.
 Number of heads per toss(xi) 0 1 2 3 4 5 No. of tosses (fi) 38 144 342 287 164 25

3.182
2.472
2.564
4.567

Q 2: Find the mean of first 10 odd natural numbers.
13
9
10
11

Q 3: Find the arithmetic mean of the following distribution
 xi 10 15 20 25 30 35 40 fi 4 6 8 18 6 5 3

29.8
12.4
24.3
20.5

Q 4: Find out the missing value of the variate for following distribution whose mean is 31.87.
 xi 12 20 27 33 ? 54 fi 8 16 48 90 30 8

31
48
35
42

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