Chapter 2, Problem 18CQ

Housing Arrangements A questionnaire on housing arrangements showed this information obtained from 25 respondents. Construct a frequency distribution for the data (H = house, A = apartment, M = mobile home, C = condominium). These data will be used in Exercise 19.

To determine

To construct: The frequency distribution of the given data.

Answer to Problem 18CQ

The frequency distribution for given data is shown below,

Housing arrangements	Tally	Frequency (f)	Percentage
H	$\cancel{\left|\right|\left|\right|}|$	6	24
A	$\cancel{\left|\right|\left|\right|}$	5	20
M	$\cancel{\left|\right|\left|\right|}|$	6	24
C	$\cancel{\left|\right|\left|\right|}\left|\right||$	8	32
TOTAL		25	100

Explanation of Solution

Given info:

A questionnaire was carried out on the housing arrangements and information from 25 respondents was obtained. Here, H is house, C is condominium, M is mobile home and A is apartment. The data is:

H	C	H	M	H	A	C	A	M
C	M	C	A	M	A	C	C	M
C	C	H	A	H	H	M

Calculation:

Since the given data is categorical so we have to construct categorical frequency distribution.

Make a table with four columns as shown below,

Housing arrangements	Tally	Frequency (f)	Percentage

Count the number of the data and tally in tally column.

Count the tallies and write in frequency column.

Housing arrangements	Tally	Frequency (f)
H	$\cancel{\left|\right|\left|\right|}|$	6
A	$\cancel{\left|\right|\left|\right|}$	5
M	$\cancel{\left|\right|\left|\right|}|$	6
C	$\cancel{\left|\right|\left|\right|}\left|\right||$	8
TOTAL		25

The frequency for every housing arrangement should be converted to percentage with the help of the formula,

$\text{Percentage}=\left(\frac{f}{n}\times 100\right)\%$

Where,

• $f$ is the frequency of the data.
• $n$ is the total number of the frequency.

Substitute 6 for $f$ and 25 for the $n$ in the formula to calculate the percentage for H,

$\begin{array}{c}\text{Percentage}=\left(\frac{6}{25}\times 100\right)\%\\ =\left(0.24\times 100\right)\%\\ =24\%\end{array}$

The percentage for the H is 24.

Substitute 5 for $f$ and 25 for the $n$ in the formula to calculate the percentage for A,

$\begin{array}{c}\text{Percentage}=\left(\frac{5}{25}\times 100\right)\%\\ =\left(0.20\times 100\right)\%\\ =20\%\end{array}$

The percentage for the A is 20.

Substitute 6 for $f$ and 25 for the $n$ in the formula to calculate the percentage for M,

$\begin{array}{c}\text{Percentage}=\left(\frac{6}{25}\times 100\right)\%\\ =\left(0.24\times 100\right)\%\\ =24\%\end{array}$

The percentage for M is 24.

Substitute 8 for $f$ and 25 for the $n$ in the formula to calculate the percentage for C,

$\begin{array}{c}\text{Percentage}=\left(\frac{8}{25}\times 100\right)\%\\ =\left(0.32\times 100\right)\%\\ =32\%\end{array}$

The percentage for C is 32.

Place the percentage value of H, A, M and C in fourth column to construct the frequency distribution shown below,

Housing arrangements	Tally	Frequency (f)	Percentage
H	$\cancel{\left|\right|\left|\right|}|$	6	24
A	$\cancel{\left|\right|\left|\right|}$	5	20
M	$\cancel{\left|\right|\left|\right|}|$	6	24
C	$\cancel{\left|\right|\left|\right|}\left|\right||$	8	32
TOTAL		25	100

Thus from the frequency distribution housing arrangement for the C is more than other type of housing arrangements.