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]

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Solution

Table: 1 Mark each
Application: 1 Mark

$\begin{matrix} Marks & No. of Students 0 - 10 & 5 10 - 20 & 5 20 - 30 & 13 30 - 40 & 8 40 - 50 & 9 \end{matrix}$

$\begin{matrix} Class Interval & x_{i} & f_{i} & f_{i} x_{i} 0 - 10 & 5 & 5 & 25 10 - 20 & 15 & 5 & 75 20 - 30 & 25 & 13 & 325 30 - 40 & 35 & 8 & 280 40 - 50 & 45 & 9 & 405 \end{matrix}$

$\sum f_{i} = 40$ & $\sum f_{i} x_{i} = 1110$

Mean
$= \frac{1110}{40}$

$= 27.75$

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Similar questions

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

$\begin{matrix} M a r k s & N o . o f S t u d e n t s B e l o w 10 & 5 B e l o w 20 & 10 B e l o w 30 & 23 B e l o w 40 & 31 B e l o w 50 & 40 \end{matrix}$

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

(ii) Find the mean.

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.

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 data gives the marks obtained by students in an exam.

$\begin{matrix} Class interval & Frequency B e l o w 10 & 5 B e l o w 20 & 10 B e l o w 30 & 23 B e l o w 40 & 31 B e l o w 50 & 45 B e l o w 60 & 49 \end{matrix}$

(i)Convert the cumulative distribution to a regular distribution.

(ii)Calculate the mode. [3 MARKS]

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The following table gives the marks obtained by the students of a class in an exam out of 50. MarksNo. of StudentsBelow 105Below 2010Below 3023Below 4031Below 5040 (i) Convert the cumulative frequency distribution into a regular frequency distribution. (ii) Find the mean. [3 MARKS]

Table: 1 Mark each Application: 1 Mark MarksNo. of Students0−10510−20520−301330−40840−509 Class Intervalxififixi0−10552510−201557520−30251332530−4035828040−50459405 ∑fi=40 & ∑fixi=1110 Mean =111040 =27.75