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Byju's Answer

Standard X

Mathematics

Best Suited Measure of Central Tendency in Different Cases and the Empirical Relationship between Them

The given dis...

Question

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
Runs scored
Number of batsmen
$3000 - 4000$
$4$
$4000 - 5000$
$18$
$5000 - 6000$
$9$
$6000 - 7000$
$7$
$7000 - 8000$
$6$
$8000 - 9000$
$3$
$9000 - 10000$
$1$
$10000 - 11000$
$1$
Find the mode of the data.

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Solution

Mode: The class which have highest frequency.
In this case, class interval $4000 - 5000$ is the modal class.

Now,
Lower limit of modal class, $l = 4000, h = 1000, f_{1}, = 18, f_{0} = 4, f_{2} = 9$

We know that,
Mode $= l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h$

$= 4000 + (\frac{18 - 4}{2 (18) - 4 - 9}) \times 1000$

$= 4000 + (\frac{14}{36 - 13}) 1000$

$= 4000 + (\frac{14}{23}) \times 1000$

Mode $= 4680.7$
Hence, the mode of the given data is $4608.7$ runs.

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Similar questions

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored	Number of batsmen
3000 − 4000	4
4000 − 5000	18
5000 − 6000	9
6000 − 7000	7
7000 − 8000	6
8000 − 9000	3
9000 − 10000	1
10000 − 11000	1

Find the mode of the data.

Q. The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored	Number of batsman	Runs scored	Number of Batsman
3000−4000 4000−5000 5000−6000 6000−7000	4 18 9 7	7000−8000 8000−9000 9000−10000 10000−11000	6 3 1 1

Find the mode of data.

Q. The following data shows the runs scored by different batsmen. Find the modal number of runs scored by the batsmen.

\begin{matrix} Runs Scored & Number of batsmen 3000 - 4000 & 4 4000 - 5000 & 18 5000 - 6000 & 9 6000 - 7000 & 7 7000 - 8000 & 6 8000 - 9000 & 3 9000 - 10000 & 1 10000 - 11000 & 1 \end{matrix}

Question 5
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

$\begin{matrix} N u m b e r o f s t u d e n t s p e r t e a c h e r & N u m b e r o f s t a t e s / U . T 3000 - 4000 & 4 4000 - 5000 & 18 5000 - 6000 & 9 6000 - 7000 & 7 7000 - 8000 & 6 8000 - 9000 & 3 9000 - 10000 & 1 10000 - 11000 & 1 \end{matrix}$

Find the mode of the data.

Question 5
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

$\begin{matrix} Runs scored & N u m b e r o f b a t s m e n 3000 - 4000 & 4 4000 - 5000 & 18 5000 - 6000 & 9 6000 - 7000 & 7 7000 - 8000 & 6 8000 - 9000 & 3 9000 - 10000 & 1 10000 - 11000 & 1 \end{matrix}$

Find the mode of the data.

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Runs scored	Number of batsmen
$3000 - 4000$	$4$
$4000 - 5000$	$18$
$5000 - 6000$	$9$
$6000 - 7000$	$7$
$7000 - 8000$	$6$
$8000 - 9000$	$3$
$9000 - 10000$	$1$
$10000 - 11000$	$1$

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. Runs scoredNumber of batsmen3000−400044000−5000185000−600096000−700077000−800068000−900039000−10000110000−110001Find the mode of the data.