Question

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Answer 1

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

Given that,

↝ The class marks of a distribution are: 25, 35, 45, 55, 65

Here,

↝ The class marks are uniformly arranged.

Since,

↝ The class size is the difference between any two consecutive class marks.

Therefore, Class size = 35 - 25 = 10

We know,

If m is the class mark and h is its class size, then the lower class limits and upper limits is given by

$\boxed{ \tt{ \: Lower \: limit = m - \frac{h}{2}}}$

and

$\boxed{ \tt{ \: Upper \: limit = m + \frac{h}{2}}}$

Tʜᴜs,

Lower and upper limit of the first class are 25 - 5 and 25 + 5, i.e. 20 and 30.

Therefore, first class interval is 20 - 30.

So, Let we first convert the given data in to continuous series using the above concept

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c}\sf Class\: interval&\sf Frequency\: (f)&\\\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}\\\sf 20 - 30&\sf 7\\\\\sf 30 - 40 &\sf 15\\\\\sf 40-50 &\sf 18\\\\\sf 50 - 60&\sf 12\\\\\sf 60-70&\sf 8\\\frac{\qquad}{}&\frac{\qquad}{}\\\sf & \sf & \end{array}}\end{gathered}\end{gathered}\end{gathered}$

[ Please check the histogram in Attachment ]