How to Calculate for Grouped, Ungrouped Data and Solved Questions

Mean method: See right here what’s imply, its definition and its method. Also, get solved examples of calculation of imply for grouped and ungrouped information utilizing direct imply method and assumed imply methodology.

Formula of imply: In statistics, “mean” is a measure of central tendency, calculated by summing all of the values ​​in a dataset and dividing by the variety of information factors. The single numerical worth calculated by the imply method represents the typical or typical worth within the dataset which is a key descriptive statistic. In this text, we are going to be taught in regards to the that means of imply, imply definition and method for grouped and ungrouped information, properties of imply, solved examples and follow questions.

Mean Definition: What is Mean?

Mean definition: According to NCERT textbook, “Mean is the value which is obtained by adding all the values ​​and dividing it by the number of observations”.

Therefore, imply is the typical of the values ​​given within the dataset.

arithmetic common

When we speak about statistical imply, there are primarily three sorts of imply, specifically arithmetic imply, geometric imply and harmonic imply. The arithmetic imply, the commonest, is the sum of all given values ​​divided by the rely of all values.

Connected: Mode Formula: How to Calculate, Examples with Solutions

imply method

Mean = (sum of values ​​in dataset/rely of values)

In quick, if the sum of values ​​in a dataset is x and the rely of values ​​is n, we are able to write

Mean method = ∑x/n

imply mark

represents the imply X̄ or X occasions.

So, whenever you see the image X̄, it means:

X̀

tips on how to discover imply

It is simple to seek out the imply of a given dataset by utilizing the imply method and substituting with the proper values. However, the method of discovering the imply of ungrouped information is barely totally different from discovering the imply worth of grouped information.

Connected: Median formula: how to calculate, examples with solutions

How to seek out the imply of ungrouped information?

In ungrouped information, values ​​are supplied individually and aren’t grouped into any class or interval.

To discover the imply of ungrouped information,

Step 1: Calculate the sum of all values ​​(x1 + x2 + x3 + … + xn)

Step 2: Divide by the variety of values ​​supplied (n)

solved instance

Find the imply of first 5 pure numbers.

Solution:

Dataset: 1,2,3,4,5

imply = ∑x/n

= (1+2+3+4+5)/ 5

= 15/5

=3

How to seek out the imply of grouped information?

Grouped information happens when a dataset is split into class intervals. Mean for grouped information might be calculated utilizing direct methodology, assumed imply methodology and section deviation methodology.

Find the imply utilizing direct methodology

step 1: Create a desk with 4 columns: Column 1 – Class Intervals, Column 2 – Frequencies (FI), Column 3 – Class Symbols xi (corresponding) and Column 4 – xifi (corresponding product of Column 2 and Column 3).

step 2: Calculate the imply by the method ∑xifi/∑fi

Here, the category mark xi is the center worth of the interval. That is, xi = (higher restrict) + (decrease restrict) / 2.

solved instance

Question: Calculate the imply.

Weight (in kg)	40 – 44	44-48	48 – 52
frequency	10	20	30

Solution,

Weight (in kg)	frequency(fi)	midpoint (xi)	fi × xi
40 – 44	10	42	420
44-48	20	46	920
48 – 52	30	50	1500
	∑fi = 60		∑fi xi = 2840

Hence imply = ∑fi xi/∑fi

= 2840/60

= 47.33

Thus, the typical weight of the given information is 47.34 kg.

Find the imply utilizing assumed imply methodology

step 1: Create a desk with 5 columns: Column 1 – class intervals, Column 2 – frequencies (fi) Column 3 – class factors xi, Column 4 – corresponding deviations di = xi – estimated imply a i.e. and Column 5 – xifi (corresponding product of columns ) 2 and column 3)

step 2: Calculate the imply by the method ∑xifi/∑fi

Here, the assumed imply A is the central worth from the category marks.

solved instance

Question: Calculate the imply utilizing the approximate imply methodology.

Weight (in kg)	40 – 44	44-48	48 – 52
frequency	10	20	30

Solution,

Let A method 50.

Weight (in kg)	frequency(fi)	midpoint (xi)	Deviation (di = xi – A)	fi × di
40 – 44	10	42	42-50=-8	-80
44-48	20	46	46-50=-4	-80
48 – 52	30	50	50-50=0	0
	∑fi = 60			∑fi di = -160

Thus, imply = A + (∑fi di)/∑fi

= 50 + (-160)/60 = 47.34

Thus, the typical weight of the given information utilizing assumed imply methodology is 47.34 kg.

properties of imply

The imply has a number of essential properties in statistics:

1. The imply is delicate to all values ​​within the dataset.
2. The imply is the equilibrium level of the dataset i.e., if the information values ​​had been positioned on a quantity line, the imply can be the purpose at which the information distribution is balanced.
3. Mean is the typical of a dataset obtained by including the values ​​in a dataset and dividing by the whole variety of values.
4. If every remark in a dataset is elevated by the identical quantity, the imply of the brand new observations may also be elevated by the identical quantity.
5. If every remark within the dataset is decreased by the identical quantity, the imply of the brand new observations may also improve by the identical quantity.

follow issues

1. Find the imply of the primary 10 prime numbers.
2. Find the imply of first 5 multiples of 5.
3. Calculate the typical weight for the next bodybuilder weight information utilizing the direct methodology.

Weight (in kg)	60 – 62	62 – 64	64 – 66	66 – 68	68-70	70 – 72
frequency	3	6	9	12	8	2

4. Calculate the imply scores for the next scholar report information utilizing the assumed imply methodology.

factors scored	99-90	89-80	79-70	69 – 60	59 – 50	49 – 40
frequency	2	6	9	12	8	2