Q.Calculate A.M. for the data : 30, 20, 32, 16, 27

The arithmetic mean is the sum of the observations divided by their number. Here the sum is 125 and there are 5 observations, so the mean is 25.

Data

30, 20, 32, 16, 27

Method

Arithmetic Mean = (Sum of all observations) / (Number of observations)

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The arithmetic mean (A.M.) of 30, 20, 32, 16 and 27 is 25, obtained by dividing the sum of the observations (125) by the number of observations (5).

Method

The arithmetic mean by the direct method is found by dividing the sum of all the observations by the total number of observations.

Arithmetic Mean = Sum of all observations / Number of observations.

Working

Step 1 — Add the observations:

30 + 20 + 32 + 16 + 27 = 125.

Step 2 — Count the number of observations:

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Arithmetic mean (the simple average) is found by adding all the values in a data set and dividing the sum by the number of values. It is the most widely used measure of central tendency and represents the typical or central value of the data.

Meaning

Arithmetic mean is the value obtained by dividing the sum of all the observations by the total number of observations. It is what is ordinarily called the average.

For an ungrouped series:

Arithmetic Mean = (Sum of all the values) / (Number of values)

For a frequency distribution:

Arithmetic Mean = (Sum of f multiplied by X) / (Sum of f), where f is the frequency and X is the value.

For example, the arithmetic mean of 10, 20 and 30 is (10 + 20 + 30) / 3 = 60 / 3 = 20.

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The arithmetic mean is a measure of central tendency found by dividing the sum of all the observations in a series by the number of observations. It is the most widely used average and represents the series by a single value.

Meaning

The arithmetic mean, commonly called the average, is the most important and widely used measure of central tendency. It is defined as the sum of all the values (items) in a series divided by the number of items:

Arithmetic Mean = Sum of all the observations / Total number of observations.

For example, if a student scores 40, 50 and 60 marks in three tests, the arithmetic mean is (40 + 50 + 60) divided by 3 = 150 / 3 = 50 marks.

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