Question

A student noted that the number of cars passing through the spot on the road for $200$ periods each of $10$ minutes and summarized in a table given below. Find the mode of the data.

Number of cars	5-10	10-15	15-20	20-25	25-30	30-35	35-40
frequency	12	24	15	10	60	55	25

• A. 15.5
• B. 20.5
• C. 25.45
• D. 19.4

Answer 1

The correct option is C 25.45

Here frequency of class interval $25-30$ is maximum.
So, it is the modal class
Now, $l=$ lower limit of modal class $=25$
$f_1$ $=$ frequency of modal class $=60$
$f_0$ $=$ frequency of class preceding the modal class $=10$
$f_2$ $=$ frequency of class succeeding the modal class $=55$
$h=$ class interval width $=5$
So, Mode $=$ $l+(\frac{f_1-f_2}{2f_1-f_0-f_2}\times h)$
$=$ $25+(\frac{60-55}{2\times 60-10-55}\times 5)$
$=25+0.4545$
$=25.45$
Mode $=25.45$