Question

25.) Prepare a frequency distribution table to the following data with class interval marks secured less than 10 less than 20 less than 30 less than40 less than 50 no of students 8 19 26 42 50​

Answer 1

$\large\underline{\sf{Solution-}}$

Given data is

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \small\boxed{\begin{array}{c |c} \tt{Marks} & \tt{Number\:of\:students} \\ \dfrac{\qquad\qquad}{ \sf Less\:than \: 10} &\dfrac{\qquad\qquad}{ \sf 8} & \\ \dfrac{\qquad\qquad}{ \sf Less\:than \: 20} &\dfrac{\qquad\qquad}{ \sf 19} & \\ \dfrac{\qquad\qquad}{ \sf Less\:than \: 30} &\dfrac{\qquad\qquad}{ \sf 26} & \\ \dfrac{\qquad\qquad}{ \sf Less\:than \: 40} &\dfrac{\qquad\qquad}{ \sf 42} & \\ \dfrac{\qquad\qquad}{ \sf Less\:than \: 50} &\dfrac{\qquad\qquad}{ \sf 50} &\end{array}} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

So, frequency distribution table is as follow :-

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \small\boxed{\begin{array}{c |c} \tt{Marks} & \tt{Number\:of\:students} \\ \dfrac{\qquad\qquad}{ \sf 0 \: - \: 10} &\dfrac{\qquad\qquad}{ \sf 8} & \\ \dfrac{\qquad\qquad}{ \sf 10 \: - \: 20} &\dfrac{\qquad\qquad}{ \sf 19 - 8 = 11} & \\ \dfrac{\qquad\qquad}{ \sf 20 \: - \: 30} &\dfrac{\qquad\qquad}{ \sf 26 - 19 = 7} & \\ \dfrac{\qquad\qquad}{ \sf 30 \: - \: 40} &\dfrac{\qquad\qquad}{ \sf 42 - 26 = 16} & \\ \dfrac{\qquad\qquad}{ \sf 40 \: - \: 50} &\dfrac{\qquad\qquad}{ \sf 50 - 42 = 8} &\end{array}} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

Hence, the frequency distribution table is

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \small\boxed{\begin{array}{c |c} \tt{Marks} & \tt{Number\:of\:students} \\ \dfrac{\qquad\qquad}{ \sf 0 \: - \: 10} &\dfrac{\qquad\qquad}{ \sf 8} & \\ \dfrac{\qquad\qquad}{ \sf 10 \: - \: 20} &\dfrac{\qquad\qquad}{ \sf 11} & \\ \dfrac{\qquad\qquad}{ \sf 20 \: - \: 30} &\dfrac{\qquad\qquad}{ \sf 7} & \\ \dfrac{\qquad\qquad}{ \sf 30 \: - \: 40} &\dfrac{\qquad\qquad}{ \sf 16} & \\ \dfrac{\qquad\qquad}{ \sf 40 \: - \: 50} &\dfrac{\qquad\qquad}{ \sf 8} &\end{array}} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

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Additional Information :-

1. Mean using Direct Method

$\boxed{ \rm{ \:Mean = \dfrac{ \sum f_i x_i}{ \sum f_i} \: }}$

2. Mean using Short Cut Method

$\boxed{ \rm{ \:Mean = A + \dfrac{ \sum f_i d_i}{ \sum f_i} \: }}$

3. Mean using Step Deviation Method

$\boxed{ \rm{ \:Mean = A + \dfrac{ \sum f_i u_i}{ \sum f_i} \times h \: }}$

Answer 2

Answer:

The following table is frequency distribution table.

ClassInterval  Frequency

5−10  0

10−15  15

15−20  20

20−30  30

30−35  35

35−40  40

Step-by-step explanation: