Question

The heights of 200 adults were recorded and divided into two categories. Which two way frequency table correctly shows the marginal frequencies?

Answer 1

Total men is 12 + 86 = 98

If 200 people were surveyed, that means the number of women should be 200 - 98 = 102.

Table B is the only one with 102 total women.

Answer 2

The two way frequency table showing the marginal frequency for the given data is Option B:

$\begin{array}{cccc}&6' \: \rm or \: over&\rm Under \: 6' & \rm Total \\\rm Male&12&86 & 98\\\rm Female&3&99 & 102\\ \rm Total & 15 & 185 & 200 \end{array}$

How to calculate marginal frequency for a given two dimensional data values?

Marginal (on the margin) frequencies are sum of all joint frequencies for a given row or for a given column. They care for a specific category and sum all of their frequencies for the second dimension (that means, they do not differentiate between values of second dimension  and just take the total frequency of the single considered category.

For the given condition, it is known that  there are 200 people. In the given table, let the count of females under 6 feet be $x$

Then we have:

$200 = 12 + 3 + 86 + x\\x = 99$

Thus, the complete table will be

$\begin{array}{ccc}&6' \: \rm or \: over&\rm Under \: 6' \\\rm Male&12&86\\\rm Female&3&99\end{array}$

Now, calculating marginal frequencies:

Two dimensions are there. One dimension differentiates between genders and one dimension differentiates between height under 6', or 6' or over

For first dimension(gender):

• Case 1: Male:

Joining all frequency over height dimension, the total of frequencies is

12 + 86 = 98

• Case 2: Female:

Joining all frequency over height dimension, the total of frequencies is

3 + 99 = 102

For second dimension(height):

• Case 1: 6' or over

Joining all frequency over Gender dimension, the total of frequencies is

12 + 3 = 15

• Case 2: Under 6'

Joining all frequency over Gender dimension, the total of frequencies is

86 + 99 = 185

Thus, the marginal frequencies will be given as said above. They usually lie on the margin of the table, named as Total.

The two way table will be

$\begin{array}{cccc}&6' \: \rm or \: over&\rm Under \: 6' & \rm Total \\\rm Male&12&86 & 98\\\rm Female&3&99 & 102\\ \rm Total & 15 & 185 & 200 \end{array}$

Thus,

The two way frequency table which correctly shows the marginal frequency for the given data is given by

Option B:

$\begin{array}{cccc}&6' \: \rm or \: over&\rm Under \: 6' & \rm Total \\\rm Male&12&86 & 98\\\rm Female&3&99 & 102\\ \rm Total & 15 & 185 & 200 \end{array}$

Learn more about marginal frequencies here:

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