Question

explain why we need to learn how to solve or get the central tendency of a given data​

Answer 1

Step-by-step explanation:

Answer:-

Central Tendency of Data - This generally refers to the measure of a certain pr given data in statistics. We, in combination often know it as Mean, Median and Mode as well.

So, the whole summary is given, with all the old versus new formulas.

So, Let's Begin!

Mean- First, when we come across this term, first thing in our mind is average. Now, we will compare average - ability with mean.

$\sf{Average = \dfrac{Sum \ of \ Total \ Obs.}{No. \ of \ total \ Obs.}}$

Obs. means observation.

We can also calculate mean in few steps like Step Deviation method, Assumed mean method.

$\sf{x = a + \bar{d}}$

• Where a is assumed mean.

$\sf{\bar{d} = \dfrac{ \Sigma \ f_i d_i}{ \Sigma \ f_i}}$

Now, coming to step deviation method:-

$\sf{\bar{x} = \dfrac{ \Sigma \ f_i d_i \times c }{ \Sigma \ f_i}}$

Where d is equal to $\rm{\dfrac{x-a}{c}}$

Median - Which is used to find the mid value of a given table.

Cumulative Frequency Comtinuous addition of values from upper to lower case or vice versa.

$\rm{ Median = l + \dfrac{ \dfrac{n}{2} - c.f}{f} \times h}$.

And empirical formula

Mode = 3 Median - 2 mean.

Answer 2

First of all let's know what is Central Tendency

• The central tendency is stated as the statistical measure that represents the single value of the entire distribution or a dataset.

Also know these 5 things / categories

1. Mean
2. Mode
3. Median
4. Step Deviation Method
5. Assumed Mean Method

Definitions with examples and its Formula

MEAN :- Add up all the Numbers, then divide by how many numbers there are.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Example :- Mean of 6, 11, 7

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀6 + 11 + 7 = 24

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 24/3 = 8

Formula :- $m = \frac{sum \: of \: the \: terms \: }{number \: of \: terms \: }$

MODE :- Put the Numbers in order, Then count how many of each number. A number which appears most often is the Mode.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Example :- Mode of 3, 3, 6, 9, 15, 15, 15, 27, 27, 37, 48.

15 is the mode since it is appearing more number of times.

Formula / How to :- 3 Median - 2 Mean = Mode

MEDIAN :- Arrange your numbers in numerical order.

Count how many numbers you have.

If you have an odd number, divide by 2 and round up to get the position of the median number.

If you have an even number, divide by 2.

Go to the number in that position and average it with the number in the next higher position to get the median.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Example :- Meadian of 4, 1, 7 is 4 as we put the numbers in order, The number 4 will be in middle. (1, 4, 7)

Formula :- $\rm{ Median = l + \dfrac{ \dfrac{n}{2} - c.f}{f} \times h}$

STEP DEVIATION METHOD :- $\sf{\bar{x} = \dfrac{ \Sigma \ f_i d_i \times c }{ \Sigma \ f_i}}$

ASSUMED MEAN METHOD :- $\sf{\bar{d} = \dfrac{ \Sigma \ f_i d_i}{ \Sigma \ f_i}}$