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\[\begin{array}{*{20}{c}}

{Marks}&{0 - 20}&{20 - 40}&{40 - 60}&{60 - 80}&{80 - 100}&{Total} \\

{Frequency}&9&a&{40}&b&{15}&{100}

\end{array}\]

The value of b is twice the value of a. Find their values and draw their histogram.

Answer
Verified

We will eventually solve these both equations to get the required values and put the values in the table and then create a histogram.

We are provided in the question that:- the value of b is twice the value of a.

This statement is equivalent to b = 2$ \times $a

So, we have:- b = 2a ……(1)

Now, we also know that there are a total of 100 students. So, the sum of all the students in each category of marks will result in 100.

Hence, 9 + a + 40 + b + 15 = 100

Clubbing all the numeric values on L.H.S. to simplify the expression, we get:-

a + b + (9 + 40 + 15) = 100

Simplifying the expression, we see that:-

a + b + 64 = 100

Taking 64 to R.H.S, we get:-

a + b = 100 – 64

Simplifying it further, we will get:-

a + b = 36 …….(2)

Now, we have got two equations (1) and (2) with 2 unknown variables a and b.

Putting (1) in (2), we will have:-

a + 2a = 36

Simplifying the L.H.S, we will get:-

3a = 36

Taking 3 on R.H.S, we will get:-

a = $\dfrac{{36}}{3} = 12$

Hence, we get a = 12.

Putting this value of a in (1),

b = 2a = 2$ \times $12 = 24

Thus, we have a = 12 and b = 24.

Now, let us draw the histogram based on the given data and the found values: