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.

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Solution

Here, we observe that 10 students have scored marks below 10 i.e., it lies between class interval 0-10. Similarly, 50 students have scored marks below 20. So, 50-10=40 students lies in the interval 10-20 and so on. The table of a frequency distribution for the given data is
$\begin{matrix} C l a s s i n t e r v a l & N u m b e r o f s t u d e n t s 0 - 10 & 10 10 - 20 & 50 - 10 = 40 20 - 30 & 130 - 50 = 80 30 - 40 & 270 - 130 = 140 40 - 50 & 440 - 270 = 170 50 - 60 & 570 - 440 = 130 60 - 70 & 670 - 570 = 100 70 - 80 & 740 - 670 = 70 80 - 90 & 780 - 740 = 40 90 - 100 & 800 - 780 = 20 \end{matrix}$

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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.

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 frequency distribution table for the data.

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.

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. Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table.

Weight (in kg)	No. of students
Below 25 Below 30 Below 35 Below 40 Below 45 Below 50 Below 55 Below 60 Below 65 Below 70	0 24 78 183 294 408 543 621 674 685

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