Arithmetic Mean Given Frequency Values

In this class, We discuss Arithmetic Mean Given Frequency Values.

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The reader should have prior knowledge of the measure of central tendency. Click Here.

Arithmetic Mean: is one of the ways to calculate a measure of central tendency.

Example:

X1, X2, X3, . . . Xn is the set of values.

Then Arithmetic mean X’ = (X1 + X2 + . . . + Xn)/n

n is number of data values.

Example:

Given 7,6, 8, 10, 13, 14

AM = (7 + 6 + 8 + 10 + 13 + 14)/6

AM = 9.66

Arithmetic Mean Given Frequencies:

Given below is the football game goal data.

The above table shows two players who make one goal.

Frequency shows how many players.

The goal column shows the number of goals.

Five players make two goals.

If the data is not in the form of frequencies, The data looks as 1,1,2,2,2,2,2,3,3..

Two players made one goal. So we put two 1’s in the data.

Arithmetic mean: (1 + 1+ 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 4 + 4 + 5)/14

The above arithmetic mean is provided in the equation X’ = (Σ XiFi) / ΣFi.

AM = X’ = (2*1 + 2*5 + 3 * 4 + 4 * 2 + 5 * 1)/(2+ 5 + 4 + 2 + 1)

X’ = 2.64

Most of the players made around 3 goals.

Example 2:

The below table shows the frequencies of parking hours.

The above table shows fifteen customers park one hour.

Frequency shows the number of customers.

X’ = (15 * 1 + 27 * 2 + 8 * 3 + 5 *4)/(15 + 27 + 8 + 5)

X’ = 2.05

The mean value says most customers are parking for around two hours.