For the following distribution- the modal class is- Marks Number of students- Below 10 3- Below 20 12- Below 30 27- Below 40 57- Below 50 75- Below 60 80- - -2 Marks-

[ Marks amp; Number of students amp; Cumulative frequency; Below 10 amp;3=3 amp;3; ...

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Standard X

Mathematics

Finding Mode for Grouped Data When Class Intervals Are Given

For the follo...

Question

For the following distribution, the modal class is

$\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s B e l o w 10 & 3 B e l o w 20 & 12 B e l o w 30 & 27 B e l o w 40 & 57 B e l o w 50 & 75 B e l o w 60 & 80 \end{matrix}$

[2 Marks]

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Solution

$\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s & C u m u l a t i v e f r e q u e n c y B e l o w 10 & 3 = 3 & 3 10 - 20 & (12 - 3) = 9 & 12 20 - 30 & (27 - 12) = 15 & 27 30 - 40 & (57 - 27) = 30 & 57 40 - 50 & (75 - 57) = 18 & 75 50 - 60 & (80 - 75) = 5 & 80 \end{matrix}$

[1 Mark]

Here, we see that the highest frequency is 30, which lies in the interval 30 - 40.

$∴$ The modal class is 30 - 40. [1 Mark]

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Similar questions

Given below is a cumulative frequency distribution showing the marks secured by $50$ students of a class: Marks Below $20$ , Below $40$ , Below $60$ , Below $80$ , Below $100$ : Number of students: $17, 22, 29, 37, 50$ respectively. Form the frequency distribution table for the data.

Q. Question 10
The following table shows the cumulative frequency distribution of marks of 800 students in an examination.

\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s B e l o w 10 & 10 B e l o w 20 & 50 B e l o w 30 & 130 B e l o w 40 & 270 B e l o w 50 & 440 B e l o w 60 & 570 B e l o w 70 & 670 B e l o w 80 & 740 B e l o w 90 & 780 B e l o w 100 & 800 \end{matrix}

Construct a frequency distribution table for the data above.

The distribution below gives the marks obtained by the students of a class in a test. Maximum marks being $80$ . Find the median marks of the students.

Marks Obtained	$b e l o w 10$	$b e l o w 20$	$b e l o w 30$	$b e l o w 40$	$b e l o w 50$	$b e l o w 60$	$b e l o w 70$	$b e l o w 80$
No. of students	$15$	$35$	$60$	$80$	$96$	$127$	$190$	$200$

The following table gives the marks obtained by the students of a class in an exam out of 50.

$\begin{matrix} Marks & No. of Students B e l o w 10 & 5 B e l o w 20 & 10 B e l o w 30 & 23 B e l o w 40 & 31 B e l o w 50 & 40 \end{matrix}$

(i) Convert the cumulative frequency distribution into a regular frequency distribution.

(ii) Find the mean. [3 MARKS]

Q. Question 14
Given below is a cumulative frequency distribution showing the marks secured by 50 students of a class

\begin{matrix} M a r k s & B e l o w 20 & B e l o w 40 & B e l o w 60 & B e l o w 80 & B e l o w 100 N u m b e r o f s t u d e n t s & 17 & 22 & 29 & 37 & 50 \end{matrix}

Form the frequecy distribution table for the data.

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For the following distribution, the modal class is MarksNumber of studentsBelow 103Below 2012Below 3027Below 4057Below 5075Below 6080 [2 Marks]

MarksNumber of studentsCumulative frequencyBelow 103=3310−20(12−3)=91220−30(27−12)=152730−40(57−27)=305740−50(75−57)=187550−60(80−75)=580 [1 Mark] Here, we see that the highest frequency is 30, which lies in the interval 30 - 40. ∴The modal class is 30 - 40. [1 Mark]

For the following distribution, the modal class is

$\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s B e l o w 10 & 3 B e l o w 20 & 12 B e l o w 30 & 27 B e l o w 40 & 57 B e l o w 50 & 75 B e l o w 60 & 80 \end{matrix}$

[2 Marks]