# Arithmetic Mean

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The most common representative value of a group of data is the **arithmetic mean** or the mean. To understand this in a better way, let us look at the following example:

Two vessels contain 20 litres and 60 litres of milk respectively. What is the amount that each vessel would have, if both share the milk equally? When we ask this question we are seeking the arithmetic mean. In the above case, the average or the arithmetic mean would be

Thus, each vessels would have 40 litres of milk.

The average or Arithmetic Mean (A.M.) or simply mean is defined as follows:

Mean =

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**Example 1:**

Ashish studies for 3 hours, 7 hours and 2 hours respectively on three consecutive days. How many hours does he study daily on an average?

**Solution :**

The average study time of Ashish would be

The day 1 is

Average =

Thus, we can say that Ashish studies for 4 hours daily on an average.

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**Example 2**

A batsman scored the following number of runs in six innings: 36, 35, 50, 46, 60, 48 Calculate the mean runs scored by him in an inning.

**Solution :**

Total runs = 36 + 35 + 50 + 46 + 60 + 48 =

To find the mean, we find the sum of all the observations and divide it by the number of observations.

Therefore, in this case, mean =

Thus, the mean runs scored in an innings are 45.

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## Where does the arithmetic mean lie

Consider the data in the above examples and think on the following:

- Is the mean bigger than each of the observations?

2. Is it smaller than each observation?

You will find that the mean lies in between the smallest and the greatest observations.

In particular, the mean of two numbers will always lie between the two numbers. For example the mean of 5 and 11 is

Let us now apply this idea to fractional numbers. You will find that using this idea, we can find any number of fractional numbers between two fractional numbers.

For example between

The average between

Now the average between

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## Try these

**1. Find the mean of your sleeping hours during one week**

**Solution :**

Number of days = 7

Mean:${mean}

Calculate Mean

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## Range

The difference between the highest and the lowest observation gives us an idea of the spread of the observations. This can be found by subtracting the lowest observation from the highest observation. We call the result the range of the observation. Look at the following example:

## Example

**The ages in years of 10 teachers of a school are: 32, 41, 28, 54, 35, 26, 23, 33, 38, 40**

**Solution :**

Can you arranging the ages in increasing order?

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