The following distribution shows the marks scored by $140$ students in examination. Calculate the mode of the distribution.
Marks $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$
Number of stu. $20$ $24$ $40$ $36$ $20$

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Solution

Here, class interval $20 - 30$ has maximum number of frequency.
$∴$ Modal class $= 20 - 30$
$l = 20, f_{0} = 24, f_{1} = 40, f_{2} = 36$ and $h = 10$
$M o d e = l + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times h$

$= 20 + \frac{40 - 24}{2 \times 40 - 24 - 36} \times 10$

$= 20 + 8$
$= 28$

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Q. The following table shows the marks scored by 140 students in an examination of a certain paper.

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Number of students:	20	24	40	36	20

Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

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$\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s 0 - 10 & 20 10 - 20 & 24 20 - 30 & 40 30 - 40 & 36 40 - 50 & 20 \end{matrix}$
Calculate mean marks by the step deviation method.

Q. The following table shows marks secured by 140 students in an examination:

\begin{matrix} Marks & Number of students 0 - 10 & 20 10 - 20 & 24 20 - 30 & 40 30 - 40 & 36 40 - 50 & 20 \end{matrix}

Calculate mean marks by the step deviation method.

Q. Find the mode of given data.

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$20$	$24$	$40$	$36$	$20$

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The following distribution shows the marks scored by 140 students in examination. Calculate the mode of the distribution.Marks0−1010−2020−3030−4040−50Number of stu. 20 24 40 36 20

Here, class interval 20−30 has maximum number of frequency.∴ Modal class =20−30l=20,f0=24,f1=40,f2=36 and h=10Mode=l+f1−f02f1−f0−f2×h =20+40−242×40−24−36×10 =20+8 =28

The following distribution shows the marks scored by $140$ students in examination. Calculate the mode of the distribution.
Marks $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$
Number of stu. $20$ $24$ $40$ $36$ $20$

Here, class interval $20 - 30$ has maximum number of frequency.
$∴$ Modal class $= 20 - 30$
$l = 20, f_{0} = 24, f_{1} = 40, f_{2} = 36$ and $h = 10$
$M o d e = l + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times h$

$= 20 + \frac{40 - 24}{2 \times 40 - 24 - 36} \times 10$

$= 20 + 8$
$= 28$