Question

Hey guys,

From the following cumulative frequency table, construct a frequency distribution table

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Answer 1

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

Given data is

The cumulative frequency distribution table is

$\begin{gathered} \begin{array}{|c|c|} \bf{Marks} & \bf{Number \: of \: students} \\ 0 \: and \: above & 40  \\10 \: and \: above & 28 \\20 \: and \: above & 16 \\30 \: and \: above & 10 \\40 \: and \: above & 8 \\ 50 \: and \: above  & 0 \end{array}\end{gathered}$

The frequency distribution table is as follow :-

$\begin{gathered} \begin{array}{|c|c|} \bf{Marks} & \bf{Number \: of \: students} \\ 0 - 10 & 12  \\10 - 20 & 12 \\20 - 30 & 6 \\30 - 40 & 2 \\40 - 50 & 8 \end{array}\end{gathered}$

Additional Information.:-

Formula's

Mode :-

$\boxed{{\bf{Mode = l + \bigg(\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \bigg) \times h }}}$

Mean using direct method :-

$\boxed{\bf Mean = \dfrac{ \sum f_i x_i}{ \sum f_i}}$

Mean using Short Cut Method :-

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

Mean using Step Deviation Method :-

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

Median :-

$\boxed{\bf Median= l + \Bigg \{h \times \dfrac{ \bigg( \dfrac{N}{2} - cf \bigg)}{f} \Bigg \}}$