Question

Class 9th
Mathematics
Chapter 14 - Statistics
Formulas Needed . Give 1 example for each Formuals .

Note : Don't copy, Don't spam .

Quality answer with good explanation will be Brainliest .​

Answer 1

Some of the important formulas related to Statistics are given below.

★ Data:-

Data is the information obtained by an investigator. It can be classified into two:

Primary data: The information collected by investigator on his/her own is called as primary data. Ex: Number of students in your class.

Secondary data: The information collected by investigator from a source, which already contains sensable information. Ex: Test marks scored by students in your class.

★ Range of a data:-

$\;\;\tt{\mapsto\;\; Range: \: Highest\:value - Lowest \: value}$

Subtracting lowest value from it's highest value in a data is known as range of the data.

★ Mean:-

Mean is nothing but the average of a given data. If there are n numbers and if we need to find the mean, we simply add up the n numbers and divide it by n. The formula to find the mean is:

$\;\;\bf{\mapsto\;\;Mean \: = \: \dfrac{Sum\:of\: observations}{Number\:of\: observations}}$

Example:

Find the mean of first five prime numbers.

Let us form the data according to the question:

$\;\;\tt{\mapsto\;\; Data: \: 2,3,5,7,11}$

$\;\;\tt{\mapsto\;\; Sum\:of\: observations \: = \: 2+3+5+7+11}$

$\;\;\tt{\mapsto\;\; Sum\:of\: observations \: = \: 28}$

$\;\;\tt{\mapsto\;\; Number\:of\: observations \: = \: 5}$

$\;\;\tt{\mapsto\;\;Mean \: = \: \dfrac{Sum\:of\: observations}{Number\:of\: observations}}$

$\;\;\tt{\mapsto\;\;Mean \: = \: \dfrac{28}{5}}$

$\;\;\bf{\mapsto\;\;Mean \: = \: 5.6}$

Hence, the mean of first five prime numbers is 5.6.

★ Median:-

Before finding median, don't forget to arrange the data in ascending order!!!!

If n = Odd,

$\;\;\bf{\mapsto\;\;Median \: = \: \dfrac{n+1}{2}th\: observation}$

If n = Even,

⟹ Median = {n/2 th observation + (n+1)/2 th observation} / 2

Example:

⟹ 1, 2, 3, 4, 5

From the given data, we can see that number of observations is odd. Therefore,

$\;\;\sf{\mapsto\;\;Median \: = \: \dfrac{n+1}{2}th\: observation}$

$\;\;\sf{\mapsto\;\;Median \: = \: \dfrac{5+1}{2}th\: observation}$

$\;\;\sf{\mapsto\;\;Median \: = \: \dfrac{6}{2}th\: observation}$

$\;\;\sf{\mapsto\;\;Median \: = \: 3rd \: observation}$

From the given data, third observation is 3. Therefore:

$\;\;\sf{\mapsto\;\;Median \: = \: 3}$

★ Mode:-

In a given data, we should check which number is frequently coming in that data. That number is the required mode.

Example:

⟹ 1, 1, 2, 3, 4, 4, 4, 5, 6, 7, 7, 7, 7

In the given data, 7 comes 4 times in the data, which is the highest. Hence, Mode of the given data is 7.

★ Empirical formula:-

$\;\;\tt{\mapsto\;\;Mode \: = \: 3Median - 2Mean}$

★ Tally marks:-

Refer the attachment for tally marks. Thank you.

Hope it helps!