Question

what are the three measure of
Central tendency of ungroup data
​

Answer 1

Aɴsᴡᴇʀ:-

➨ᴍᴇᴀɴ

➨ᴍᴇᴅɪᴀɴ

➨ᴍᴏᴅᴇ

ʜᴏᴘᴇ ɪᴛs ʜᴇʟᴘs ᴜʜ~

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

The three measures of the central tendency of ungrouped data are :

• $\bold{\red{mean}}$
• $\bold{\red{median}}$
• $\bold{\red{mode }}$

$\huge\bold{\underline{\underline{\red{mean}}}}$

Mean is the sum of all the measurements divided by the number of observation.

see attach image 2 for formula

Here,$\bold{\&#8721{x}}$ is the sum of all measurements and n is the number of observation.

There are two methods to find mean in an ungrouped data :-

a)Direct method

see attach image 2 for formula

b) shortcut method

see attach image 2 for formula

$\huge\bold{\underline{\underline{\red{median}}}}$

Median is that value of variable which divides the group into two equal parts

Calculation of median

• Individual series
• Discrete series
• Continuous series

Individual series

In this method firstly we have to arrange the data in an ascending order then find median.

example :

students ㅤㅤㅤㅤㅤㅤㅤheights

Aㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ151

Bㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ140

Cㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ149

Dㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ142

Eㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ147

Fㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ144

Gㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ145

Firstly we convert into ascending order

140,142,144,145,147,149,151

N=7

$median = \frac{n + 1}{2} th = \frac{7 + 1}{2} = 4th \: term$

median =145

Discrete series

is same as individual

Continuous series

In continuous series the data having intervals and a frequency are given.In this we have to find cumulative frequency and hence find median.

see figure 1 above .

$\bold{median = ( \frac{n}{2} )th \: term}}$

$\bold{\boxed{median = l + \frac{ \frac{n}{2} - CF \times h}{f}}}$

$\huge\bold{\underline{\underline{\red{mode}}}}$

mode is the value in a distribution around which the items are concentrated heavily.

or in another words observation which occurs the greatest number of times

Types of methods in mods

• Individual series
• discrete series
• continuous series

$\bold{\boxed{mode = l + \frac{f1 - fo}{2f1 - fo - f2} \times h}}$