Question

A national survey asked people, "How often do you eat out for dinner, instead of
at home?" The frequencies were as follows. Complete parts (a) through (g)

Answer 1

A relative frequency table is used to display the proportion of variables, in a tabular form.

• 3.1% of the respondents responds always
• 32.5% of the respondents responds never or rarely.

(a) Draw the Relative Frequency

To do this, we simply divide the frequency of each response by the total frequency.

The total frequency is:

$Total = 326 + 304 + 992 + 257 + 61$

$Total = 1940$

So, the calculation of the relative frequency table is as follows:

$Never = \frac{326}{1940}=0.168=16.8\%$

$Rarely = \frac{304}{1940}=0.157=15.7\%$

$Sometimes = \frac{992}{1940}=0.511=51.1\%$

$Most\ times = \frac{257}{1940}=0.132=13.2\%$

$Always = \frac{61}{1940}=0.031=3.1\%$

The relative frequency table is:

$\left[\begin{array}{ccc}{Response}&{Frequency}&{Relative\ Frequency}\\Never&326&16.8\%\\Rarely&304&15.7\%&Sometimes&992&51.1\%&Most\ Times&257&13.2\%&Always&61&3.1\%\end{array}\right]$

(b) Percentage that responds always.

From the above calculation, we have:

$Always = 3.1\%$

Hence, 3.1% responds always

(c) Percentage that responds never or rarely.

From the above calculation, we have:

$Never = 16.8\%$

$Rarely =15.7\%$

So, we have:

$Never\ or\ Rarely = Never + Rarely$

$Never\ or\ Rarely = 16.8\%+ 15.7\%$

$Never\ or\ Rarely = 32.5\%$

Hence, 32.5% responds never or rarely.

(d) The frequency bar graph

To do this, we plot the response against the frequency

See attachment for bar graph

Read more about relative frequency table at:

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