![\bold{\huge{\underline{ Solution }}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Chuge%7B%5Cunderline%7B%20Solution%20%7D%7D%7D)
<h3><u>Given </u><u>:</u><u>-</u></h3>
- We have given some information in the above table
<h3><u>To </u><u>Find </u><u>:</u><u>-</u></h3>
- We have to find the mean, median and mode of the given data.
<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u></h3>
<u>For </u><u>completion </u><u>of </u><u>table </u><u>you </u><u>should </u><u>know </u><u>the </u><u>basics </u><u>formulas </u><u>:</u><u>-</u>
- For calculating x( mid point)
![\sf{=}{\sf{\dfrac{Sum \:of\: class \:interval }{ 2}}}](https://tex.z-dn.net/?f=%5Csf%7B%3D%7D%7B%5Csf%7B%5Cdfrac%7BSum%20%5C%3Aof%5C%3A%20class%20%5C%3Ainterval%20%7D%7B%202%7D%7D%7D)
<u>That </u><u>is</u><u>, </u>
![\sf{=}{\sf{\dfrac{ = 18 + 25}{2}}}](https://tex.z-dn.net/?f=%5Csf%7B%3D%7D%7B%5Csf%7B%5Cdfrac%7B%20%3D%2018%20%2B%2025%7D%7B2%7D%7D%7D)
![\sf{=}{\sf{\dfrac{ = 43}{2}}}](https://tex.z-dn.net/?f=%5Csf%7B%3D%7D%7B%5Csf%7B%5Cdfrac%7B%20%3D%2043%7D%7B2%7D%7D%7D)
![\sf{= 21.5 }](https://tex.z-dn.net/?f=%5Csf%7B%3D%2021.5%20%7D)
[ For more calculation ,Please refer the attachment ]
- For calculating fx
- Multiply frequency and midpoint
![\sf{ fx = frequency {\times} midpoint }](https://tex.z-dn.net/?f=%5Csf%7B%20fx%20%3D%20frequency%20%7B%5Ctimes%7D%20midpoint%20%7D)
![\sf{ fx = 8 {\times} 21.5 }](https://tex.z-dn.net/?f=%5Csf%7B%20fx%20%3D%208%20%7B%5Ctimes%7D%2021.5%20%7D)
![\sf{ fx = 172 }](https://tex.z-dn.net/?f=%5Csf%7B%20fx%20%3D%20172%20%7D)
[ For more calculation please refer the attachment ]
<h3><u>Now</u><u>, </u></h3>
We have to calculate mean, median and mode of the given data
<h3>
<u>For </u><u>mean </u></h3>
We know that the,
Mean = Sum of all observation / no. of observation
<u>That </u><u>is </u>
![\sf{ Mean = }{\sf{\dfrac{ {\sigma}fx}{{\sigma}x}}}](https://tex.z-dn.net/?f=%5Csf%7B%20Mean%20%3D%20%7D%7B%5Csf%7B%5Cdfrac%7B%20%7B%5Csigma%7Dfx%7D%7B%7B%5Csigma%7Dx%7D%7D%7D)
<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>, </u>
![\sf{ Mean = }{\sf{\dfrac{ 1811 }{ 187.5}}}](https://tex.z-dn.net/?f=%5Csf%7B%20Mean%20%3D%20%7D%7B%5Csf%7B%5Cdfrac%7B%201811%20%7D%7B%20187.5%7D%7D%7D)
![\sf{ Mean = 9.65}](https://tex.z-dn.net/?f=%5Csf%7B%20Mean%20%3D%209.65%7D)
Hence, The mean of the given data is 9.65
<h3><u>For </u><u>Median </u></h3>
<u>We </u><u>know </u><u>that</u><u>,</u><u> </u><u>For </u><u>odd </u><u>numbers </u>
![\sf{ Median = l + }{\sf{\dfrac{ (n/2 - c)}{ f}}}{\sf{ h }}](https://tex.z-dn.net/?f=%5Csf%7B%20Median%20%3D%20l%20%2B%20%7D%7B%5Csf%7B%5Cdfrac%7B%20%28n%2F2%20-%20c%29%7D%7B%20f%7D%7D%7D%7B%5Csf%7B%20h%20%7D%7D)
<u>Here, </u>
![\sf{ n = }{\sf{\dfrac{ 50 + 1}{ 2}}}](https://tex.z-dn.net/?f=%5Csf%7B%20n%20%20%3D%20%7D%7B%5Csf%7B%5Cdfrac%7B%2050%20%2B%201%7D%7B%202%7D%7D%7D)
![\sf{ n = }{\sf{\dfrac{ 50 }{ 2}}}](https://tex.z-dn.net/?f=%5Csf%7B%20n%20%3D%20%7D%7B%5Csf%7B%5Cdfrac%7B%2050%20%7D%7B%202%7D%7D%7D)
![\sf{ n = 25 }](https://tex.z-dn.net/?f=%5Csf%7B%20%20n%20%3D%2025%20%7D)
- Lower limit = 34
- c = 20
- f = 14
- h = 41 - 34 = 7
<u>Subsitute </u><u>the </u><u>required </u><u>values </u><u>in </u><u>the </u><u>above </u><u>formula </u><u>:</u><u>-</u>
![\sf{ Median = 34 + }{\sf{\dfrac{ (25-20)}{ 14}}}{\sf{ 7 }}](https://tex.z-dn.net/?f=%5Csf%7B%20Median%20%3D%2034%20%2B%20%7D%7B%5Csf%7B%5Cdfrac%7B%20%2825-20%29%7D%7B%2014%7D%7D%7D%7B%5Csf%7B%207%20%7D%7D)
![\sf{ = 34 + }{\sf{\dfrac{ 5}{ 14}}}{\sf{ {\times}7 }}](https://tex.z-dn.net/?f=%5Csf%7B%20%3D%2034%20%2B%20%7D%7B%5Csf%7B%5Cdfrac%7B%205%7D%7B%2014%7D%7D%7D%7B%5Csf%7B%20%7B%5Ctimes%7D7%20%7D%7D)
![\sf{ = 34 + }{\sf{\dfrac{ 35}{ 14}}}](https://tex.z-dn.net/?f=%5Csf%7B%20%20%3D%2034%20%2B%20%7D%7B%5Csf%7B%5Cdfrac%7B%2035%7D%7B%2014%7D%7D%7D)
![\sf{ = 34 + 2.5}](https://tex.z-dn.net/?f=%5Csf%7B%20%3D%2034%20%2B%202.5%7D)
![\sf{ = 36.5 }](https://tex.z-dn.net/?f=%5Csf%7B%20%3D%2036.5%20%7D)
Hence, The median of the given data is 36.5 .
<h3><u>For </u><u>Mode </u></h3>
<u>We </u><u>know </u><u>that</u><u>, </u>
![\sf{ M= l }{\sf{\dfrac{ (f1 - fo)}{ 2f1 - fo - f2 }}}{\sf{ {\times} h }}](https://tex.z-dn.net/?f=%5Csf%7B%20M%3D%20%20l%20%7D%7B%5Csf%7B%5Cdfrac%7B%20%28f1%20-%20fo%29%7D%7B%202f1%20-%20fo%20-%20f2%20%7D%7D%7D%7B%5Csf%7B%20%7B%5Ctimes%7D%20h%20%7D%7D)
- lower limit = 34
- f1 = 14
- fo = 12
- f2 = 12
- H = 7
<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>, </u>
![\sf{ M= 34 }{\sf{\dfrac{ (14 - 12)}{ 2(14)- 12 - 12 }}}{\sf{ {\times} 7 }}](https://tex.z-dn.net/?f=%5Csf%7B%20M%3D%20%2034%20%7D%7B%5Csf%7B%5Cdfrac%7B%20%2814%20-%2012%29%7D%7B%202%2814%29-%2012%20-%2012%20%7D%7D%7D%7B%5Csf%7B%20%7B%5Ctimes%7D%207%20%7D%7D)
![\sf{ M= 34{\times}}{\sf{\dfrac{ 2}{ 28 - 24 }}}{\sf{ {\times} 7 }}](https://tex.z-dn.net/?f=%5Csf%7B%20M%3D%2034%7B%5Ctimes%7D%7D%7B%5Csf%7B%5Cdfrac%7B%202%7D%7B%2028%20-%2024%20%7D%7D%7D%7B%5Csf%7B%20%7B%5Ctimes%7D%207%20%7D%7D)
![\sf{ M= 34{\times}}{\sf{\dfrac{ 2}{ 4 }}}{\sf{ {\times} 7 }}](https://tex.z-dn.net/?f=%5Csf%7B%20M%3D%2034%7B%5Ctimes%7D%7D%7B%5Csf%7B%5Cdfrac%7B%202%7D%7B%204%20%7D%7D%7D%7B%5Csf%7B%20%7B%5Ctimes%7D%207%20%7D%7D)
![\sf{ M= 34{\times}}{\sf{\dfrac{ 1}{ 2 }}}{\sf{ {\times} 7 }}](https://tex.z-dn.net/?f=%5Csf%7B%20M%3D%2034%7B%5Ctimes%7D%7D%7B%5Csf%7B%5Cdfrac%7B%201%7D%7B%202%20%7D%7D%7D%7B%5Csf%7B%20%7B%5Ctimes%7D%207%20%7D%7D)
![\sf{ M= 34{\times}}{\sf{\dfrac{ 7}{ 2 }}}](https://tex.z-dn.net/?f=%5Csf%7B%20M%3D%2034%7B%5Ctimes%7D%7D%7B%5Csf%7B%5Cdfrac%7B%207%7D%7B%202%20%7D%7D%7D)
![\sf{ M= 34 + 3.5 }](https://tex.z-dn.net/?f=%5Csf%7B%20M%3D%2034%20%2B%203.5%20%7D)
![\sf{ M= 37.5 }](https://tex.z-dn.net/?f=%5Csf%7B%20M%3D%2037.5%20%7D)
<u>So</u><u>, </u>
Hence ,The mode of the given data is 37.5 .