Question

Calculate mode for the following data shows the number of colour pencils the students have in a class.

Colour Pencils	$0-5$	$5-10$	$10-15$	$15-20$	$20-25$	$25-30$
Number of students	$14$	$16$	$17$	$13$	$8$	$12$

• A. $11$
• B. $15$
• C. $19$
• D. $16$

Answer 1

Answer: (A)

$11$

The lower limit ( l ) of the modal class $=10,$

The class size ( h) $=5,$

The frequency $\left(f_1\right)$ of modal class $=17$,

The frequency $\left(f_0\right)$ of the class preceding the modal class $=16$,

The frequency $\left(f_2\right)$ of the class succeeding the modal class $=13.$

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

$=60+\left(\frac{17-16}{(2\times 17)-16-13}\right)\times 5$

$=10+0.2\times 5$

$=10+1$

$=11$

Therefore, mode of colour pencil students have is $11$