Question

Help pls tysm in advance

Answer 1

$\bold{\huge{\underline{ Solution }}}$

Given :-

• We have given some information in the above table

To Find :-

• We have to find the mean, median and mode of the given data.

Let's Begin :-

For completion of table you should know the basics formulas :-

• For calculating x( mid point)

$\sf{=}{\sf{\dfrac{Sum \:of\: class \:interval }{ 2}}}$

That is,

$\sf{=}{\sf{\dfrac{ = 18 + 25}{2}}}$

$\sf{=}{\sf{\dfrac{ = 43}{2}}}$

$\sf{= 21.5 }$

[ For more calculation ,Please refer the attachment ]

• For calculating fx
• Multiply frequency and midpoint

$\sf{ fx = frequency {\times} midpoint }$

$\sf{ fx = 8 {\times} 21.5 }$

$\sf{ fx = 172 }$

[ For more calculation please refer the attachment ]

Now,

We have to calculate mean, median and mode of the given data

For mean

We know that the,

Mean = Sum of all observation / no. of observation

That is

$\sf{ Mean = }{\sf{\dfrac{ {\sigma}fx}{{\sigma}x}}}$

Subsitute the required values,

$\sf{ Mean = }{\sf{\dfrac{ 1811 }{ 187.5}}}$

$\sf{ Mean = 9.65}$

Hence, The mean of the given data is 9.65

For Median

We know that, For odd numbers

$\sf{ Median = l + }{\sf{\dfrac{ (n/2 - c)}{ f}}}{\sf{ h }}$

Here,

$\sf{ n = }{\sf{\dfrac{ 50 + 1}{ 2}}}$

$\sf{ n = }{\sf{\dfrac{ 50 }{ 2}}}$

$\sf{ n = 25 }$

• Lower limit = 34
• c = 20
• f = 14
• h = 41 - 34 = 7

Subsitute the required values in the above formula :-

$\sf{ Median = 34 + }{\sf{\dfrac{ (25-20)}{ 14}}}{\sf{ 7 }}$

$\sf{ = 34 + }{\sf{\dfrac{ 5}{ 14}}}{\sf{ {\times}7 }}$

$\sf{ = 34 + }{\sf{\dfrac{ 35}{ 14}}}$

$\sf{ = 34 + 2.5}$

$\sf{ = 36.5 }$

Hence, The median of the given data is 36.5 .

For Mode

We know that,

$\sf{ M= l }{\sf{\dfrac{ (f1 - fo)}{ 2f1 - fo - f2 }}}{\sf{ {\times} h }}$

• lower limit = 34
• f1 = 14
• fo = 12
• f2 = 12
• H = 7

Subsitute the required values,

$\sf{ M= 34 }{\sf{\dfrac{ (14 - 12)}{ 2(14)- 12 - 12 }}}{\sf{ {\times} 7 }}$

$\sf{ M= 34{\times}}{\sf{\dfrac{ 2}{ 28 - 24 }}}{\sf{ {\times} 7 }}$

$\sf{ M= 34{\times}}{\sf{\dfrac{ 2}{ 4 }}}{\sf{ {\times} 7 }}$

$\sf{ M= 34{\times}}{\sf{\dfrac{ 1}{ 2 }}}{\sf{ {\times} 7 }}$

$\sf{ M= 34{\times}}{\sf{\dfrac{ 7}{ 2 }}}$

$\sf{ M= 34 + 3.5 }$

$\sf{ M= 37.5 }$

So,

• Mode = 37.5

Hence ,The mode of the given data is 37.5 .