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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 the arithmetic mean of the following distribution
xi10152025303540
fi46818653

24.3
12.4
20.5
29.8

Q 2: 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 3: If the mean of the following data is 18, find the missing frequency p.
xi10152025
fi510p8

8
4
6
7

Q 4: Find out the missing value of the variate for following distribution whose mean is 31.87.
xi12202733?54
fi8164890308

31
48
35
42

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Question 6: This question is available to subscribers only!


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