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.
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 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.
- By knowing the midpoint, you can easily calculate the elasticity for various things.
- It would help us to avoid errors.
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
- Assumed mean method
- Step derived methods
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
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.
after dividing both values you will get a mean value.
Following are the steps to find mean value by using the direct method:
The formula for the direct method is:
x = ——-
- 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)
|Class interval||fi||Class Mark (xi)||fi xi|
|0 – 10||4||5||20|
|10 – 20||10||15||150|
|30 – 40||12||35||420|
|40 – 50||6||45||270|
|Σ fi = 50||Σ fi xi = 1310|
x = ——-
Mean = (1310 / 50)
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
- By using the 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=(x1+x2 /2+ y1+y2/2)
The midpoint formula is given as:
M= upper + lower limit/2