## MEAN VALUE:

The mean value is the ratio between the sum of the values to the number of values. You can consider the mean value as the average of numbers.

## MIDPOINT:

The midpoint is the middle of the central point of any line segment. The other word used for midpoint is median.

## IMPORTANCE OF MEAN VALUE:

The mean is essentially a model of your data set. The mean is used to minimize the error prediction. Mean **produces the lowest amount of error from all other values in the data set**.

## IMPORTANCE OF MIDPOINT:

The main property of the midpoint is that it divides a line segment in ratio 1:1.

In statistics, the midpoint is defined as the average of upper and lower limits.

## ADVANTAGES OF MEAN AND MIDPOINT VALUES:

**MEAN** POINT:

- Mean represents the main value or center of the data.
- It is the arithmetic average of the data set.
- It is easy to find and saves you from hectic calculations.
- It is the right choice for further algebraic problems.
- It is error-free and is rigidly defined.

### MIDPOINT:

- By knowing the midpoint, you can easily calculate the elasticity for various things.
- It would help us to avoid errors.

## METHODS:

**METHODS TO FIND MEAN VALUE:**

The common methods which are used to find the mean value of any data set are given as:

- Direct method

### Simple method

** **The most used method for finding mean is described below:

To find the mind value, calculate the number of digits in a series and add all these digits to get the sum.

Consider we have series, i.e

**4,7,3,2 and 1**

The first step deals with adding all the 5 values

**4+7+3+2+1=17 **

** **After getting the result of adding all the 5 numbers now you can move forward towards the next step.

The next step of getting a mean value involves dividing the result of the sum of 5 values by the total number of digits.

**17/5 =3.4**

after dividing both values you will get a mean value.

### Direct method:

** **Following are the steps to find mean value by using the direct method:

The **formula** for the direct method is:

** Σfi xi**

** x = ——-**

** Σ fi**

- The first step involved finding out the
**Σ fi xi**and**Σ fi**values. - After finding the sum or
**Σ fi xi**and**Σ fi**values divide the**Σ fi xi**value with**Σ fi**value and you will get your answer.

**A frequency table can easily be created by using the number of students and their obtained marks. (As shown below)**

**Solution **

Class interval |
fi |
Class Mark (xi) |
fi xi |

0 – 10 |
4 |
5 |
20 |

10 – 20 |
10 |
15 |
150 |

20 -30 |
18 |
25 |
450 |

30 – 40 |
12 |
35 |
420 |

40 – 50 |
6 |
45 |
270 |

Σ fi = 50 |
Σ fi xi = 1310 |

** Σfi xi**

** x = ——-**

** Σ fi**

Mean = (1310 / 50)

= 26.2

### Assumed mean method

Suppose x1, x2, x3,…,xn are midpoints of n intervals and f1, f2, f3, …, fn are the respective frequencies. The formula for finding mean by the assumed mean method is:

Where **a =** assumed mean

**fi =** frequency

**di = xi – a =** deviation

**Σfi = n =** Total number of observations

**xi =** class mark = **(upper class limit + lower class limit)/2**

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## METHODS TO FIND MIDPOINT**:**

You can find midpoint whether

- By using formula

Or

- By using the graphical method

### GRAPHICAL METHOD:

The graphical method is used if you want to find a midpoint of a line segment.

To find the midpoint of any line segment, we need to follow these steps:

- Add points of x coordinates and divide them by 2.
- Add points of y coordinates and divide them by 2.

By using the graphical method you can apply the formula given below:

**M=(***x***1+***x***2 /2+*** y***1+***y***2/2)**

## FORMULA:

The midpoint formula is given as:

**M= upper + lower limit/2**

if you’re working on a school assignment involving these two topics and want to do it quick, check out the midpoint formula calculator and mean calculator.