Question

The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
$5$, $3$, $10$, $20$, $25$, $11$, $13$, $7$, $12$, $31$, $19$, $10$, $12$, $17$, $18$, $11$, $32$, $17$, $16$, $2$, $7$, $9$, $7$, $8$, $3$, $5$, $12$, $15$, $18$, $3$, $12$, $14$, $2$, $9$, $6$, $15$, $15$, $7$, $6$, $12$
How many engineers travelled distances more than 14 and less than 26?
A) $9$
B) $10$
C) $11$
D) $8$

Answer 1

In this question, we are given the distance of the residence to the place of work of 40 engineers and we have been asked the number of engineers who travelled distances more than 14 and less than 26. First, arrange the data in such a manner that it is easy to count and looks presentable. Then count the number of people written in front of distances, $14 < d < 26$. You will have your answer.

Complete step-by-step solution:
We are given the distance of the residence to the place of work of 40 engineers and we have been asked the number of engineers who travelled distances more than 14 and less than 26. We will make a tally mark chart for this purpose.

Observation	Tally Marks	Frequency
$2$
$3$
$5$
$6$
$7$
$8$
$9$
$10$
$11$
$12$
$13$
$14$
$15$
$16$
$17$
$18$
$19$
$20$
$25$
$31$
$32$

Now, we have to find out how many engineers travelled distances more than 14 and less than 26.
Once we have made this table, we have to just add the frequency written in front of the distances which lie in the interval, $14 < d < 26$.
From the table, we can see that we have to add only the following frequency:

Distances	Frequency
$15$	$3$
$16$	$1$
$17$	$2$
$18$	$2$
$19$	$1$
$20$	$1$
$25$	$1$
$\sum {f = 11}$

Hence, 11 engineers travelled distances more than 14 and less than 26.

$\therefore$ Our answer is option C) 11.

Note: It should be kept in mind that frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur. We represent the frequency by the English alphabet ‘f’. Frequency table by arranging collected date values and their corresponding frequencies. The purpose of constructing this table is to show the number of times a value occurs. We will not consider the frequency written in front of 14 as we have been asked by the engineers covering distance more than 14 and not equal to 14.