Question

Calculate the mode for the following data$:$

Daily income	$100-200$	$200-300$	$300-400$	$400-500$	$500-600$	$600-700$
Workers	$12$	$23$	$45$	$50$	$30$	$12$

• A. $410$
• B. $405$
• C. $420$
• D. $440$

Answer 1

The correct option is C $420$

Here frequency of class interval $400-500$ is maximum.

So, it is the modal class

Now, $l$ = lower limit of modal class = 400

$f_1=$ frequency of modal class $=50$

$f_0=$ frequency of class preceding the modal class $=45$

$f_2=$frequency of class succeeding the modal class $=30$

$h=$ class interval width $=100$

So, Mode $=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$

$=400+\left(\frac{50-45}{2\times 50-45-30}\right)\times 100$

$=400+\left(\frac{5}{100-75}\right)\times 100$

$=400+20$

$=420$

Mode$=420$