Name: Cumulative Frequency Table by Less Than Method
Uploaded: 2019-07-19
Duration: 6 min 42 s
Description: The sum of frequencies of a class and those of the classes preceding it is called the cumulative frequency of that class. Learn more about this by the less t...

Question

A researcher took a questionnaire to $64$ households. The grouped frequency table shows the time taken ( $t$ minutes) by various homeowners to complete a questionnaire.

Time taken $(t)$ in minutes	No. of home owners
$0 \leq t < 2$	$2$
$2 \leq t < 3$	$18$
$3 \leq t < 4$	$25$
$4 \leq t < 6$	$12$
$6 \leq t < 9$	$5$
$9 \leq t < 15$	$2$

Using a scale of $1 cm$ to represent $2 minutes$ , construct a horizontal axis for $0 \leq t < 15$ .

Using a vertical scale of $1 cm$ per $2$ units, draw a histogram to represent this data.

Accepted Answer

As the class widths are unequal, we have to find the frequency density of each class to draw the histogram. The frequency density table looks like:

Time taken in seconds

$(t)$

frequency

$0 \leq t < 2$

Class width

$(C W)$

Frequency density

$(f \div C W)$

$0 \leq t < 2$ $2$ $2$ $\frac{2}{2} = 1$

$2 \leq t < 3$ $9 \leq t < 15$ $1$ $\frac{18}{1} = 18$

$3 \leq t < 4$ $0 \leq t < 15$ $1$ $\frac{25}{1} = 25$

$4 \leq t < 6$ $12$ $2$ $\frac{12}{2} = 6$

$6 \leq t < 9$ $5$ $3$ $\frac{5}{3} = 1.67$

$9 \leq t < 15$ $2$ $6$ $\frac{2}{6} = \frac{1}{3} = 0.33$

The time in minutes is represented on $x -$ axis and corresponding frequency density is represented on $y -$ axis.
The histogram is shown below.

Karen Morrison and Nick Hamshaw Solutions for Exercise 5: Examination practice

Karen Morrison Mathematics Solutions for Exercise - Karen Morrison and Nick Hamshaw Solutions for Exercise 5: Examination practice

Questions from Karen Morrison and Nick Hamshaw Solutions for Exercise 5: Examination practice with Hints & Solutions

Learn and Prepare for any exam you want !