##
**Arithmetic
Mean (Average)**

**Arithmetic Mean (A**

**verage)**is the measure of single central value or average of the given data that represents the characteristics of entire data.

**Arithmetic Mean (A**

**verage)**is given by dividing the sum of all data by the total number of data.

####
__Arithmetic
mean (Average) for individual data__**:**

__Arithmetic mean (Average) for individual data__

**Arithmetic mean**or

**average**for individual data is given by dividing the total sum of data by the total number of data. i.e.

####
__Arithmetic
mean (Average) for discrete data__**:**

__Arithmetic mean (Average) for discrete data__

A data having some repeated value i.e. frequency is called
discrete data. To calculate the mean of repeated data, we follow the following
steps:

1. Draw a table with 3 columns.

2. Write down the items (x) in ascending order
in the first column.

3. Write the corresponding frequency (f) of
each item in the second column.

4. Find the product of each item (x) and its
frequency (f) in the third column.

5. Find the total of f column and fx column.

6. Divide the sum of fx by the sum of f i.e. N
to get the mean. i.e.

####
__Arithmetic
mean (Average) for grouped data__**:**

__Arithmetic mean (Average) for grouped data__

The data, which have class interval and frequency is called
grouped data. To calculate the mean of grouped data, we follow the following steps:

1. Draw a table with 4 columns.

2. Calculate the mid-value (m) of each class
interval by applying the formula,

3. Write down the items (m) in ascending order
in the second column.

4. Write the corresponding frequency (f) of
each item in the third column.

5. Find the product of each item (m) and its
frequency (f) in the fourth column.

6. Find the total of f column and fm column.

7. Divide the sum of fm by the sum of f i.e. N
to get the mean. i.e.

###
**Combined
mean**

We can compute a single mean from the means of different sets of
data. Such mean is called combined mean.

###
*Workout
Examples*

*Workout Examples*

*Example 1: Find the mean of data: 10, 70, 80, 40, 50, 60*

*Solution:*

*Here,*

*Data: 10, 70, 80, 40, 50, 60*

*No. of data (N) = 6*

*Mean (*

*) = ?*

*We know,*

*Example 2: Find the mean marks of:*

Marks |
10 |
20 |
30 |
40 |
50 |

No. of students |
1 |
2 |
3 |
4 |
5 |

*Solution:*

*Here,*

Marks (x) |
Frequency (f) |
f × x |

1020304050 |
12345 |
104090160250 |

N = 15 |
∑fx = 550 |

*Now,*

*Example 3: Find the value of m from the following data, if mean is 36.*

Marks |
10 |
20 |
38 |
40 |
50 |

No. of students |
1 |
2 |
m |
2 |
3 |

*Solution:*

*Here,*

Marks (x) |
Frequency (f) |
f × x |

1020384050 |
12m23 |
104038m80150 |

N = 8+m |
∑fx = 280+38m |

*Now,*

*or, 280+38m = 36(8+m)*

*or, 280+38m = 288+36m*

*or, 38m-36m = 288-280*

*or, 2m = 8*

*or, m = 8/2*

*or, m = 4*

*∴*

*The value of m is 4.*

*Example 4: Find the mean of the following data:*

Marks |
10-20 |
20-30 |
30-40 |
40-50 |
50-60 |

No. of students |
2 |
3 |
2 |
4 |
5 |

*Solution:*

*Here,*

Marks |
Mid-value (m) |
Frequency (f) |
f × m |

10-2020-3030-4040-5050-60 |
1525354555 |
23245 |
307570180275 |

N = 16 |
∑fx = 630 |

*Now,*

*Example 5: The mean weight of 25 boys is 45.6kg and that of 32 girls is 39.9kg find their mean weight.*

*Solution:*

*Here,*

*You can comment your questions or problems regarding*

**arithmetic mean**or**average**here.

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