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

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(ii) Find the mean.

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$\begin{matrix} M a r k s & N o . o f s t u d e n t s A b o v e 0 & 80 A b o v e 10 & 77 A b o v e 20 & 72 A b o v e 30 & 65 A b o v e 40 & 55 A b o v e 50 & 43 A b o v e 60 & 23 A b o v e 70 & 16 A b o v e 80 & 10 A b o v e 90 & 8 A b o v e 100 & 0 \end{matrix}$

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

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Q. The following table gives the frequency distribution of the percentage of marks obtained by 2300 students in a competitive examination.

Marks obtained (in per cent)	11−20	21−30	31−40	41−50	51−60	61−70	71−80
Number of students	141	221	439	529	495	322	153

(a) Convert the given frequency distribution into the continuous form.

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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