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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 :
    xi12131415161718
    fi13481031
  • Solution


Q 1: Find out the missing value of the variate for following distribution whose mean is 31.87.
xi12202733?54
fi8164890308

31
42
48
35

Q 2: Find the value of p, if the mean of the following distribution is 20 :
xi15171920+p23
fi2345p6

2
4
1
5

Q 3: 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)012345
No. of tosses (fi)3814434228716425

2.472
2.564
4.567
3.182

Q 4: Find the mean of first 10 odd natural numbers.
10
11
9
13

Question 5: This question is available to subscribers only!

Question 6: This question is available to subscribers only!


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