The heights of 200 adults were recorded and divided into two categories.
| | % or over | Under © |
| :----- | :-------- | :------ |
| Male | 12 | 86 |
| Female | 3 | |
Which two-way frequency table correctly shows the marginal frequencies?
A.
| | $6$ or over | Under ${}^\circ$ | Total |
| :----- | :---------- | :---------------- | :---- |
| Nale | 12 | 86 | 98 |
| Female | 3 | 99 | 102 |
| Total | 15 | 185 | 200 |
B.
| | F or over | Under $6{}^\circ$ | Total |
| :----- | :-------- | :---------------- | :---- |
| Male | 12 | 86 | 100 |
| Female | 3 | 97 | 100 |
| Total | 15 | 185 | 200 |
C.
| | ${}^\prime$ or over | Under ${}^\prime$ | Total |
| :----- | :---------------- | :------------------ | :---- |
| Nale | 12 | 86 | 98 |
| Female | 3 | 197 | 200 |
| Total | 15 | 283 | 298 |
D.
| | %${}^\prime$ or over | Under 6${}^\prime$ | Total |
| :----- | :------------------ | :------------------ | :---- |
| Male | 12 | 86 | 98 |
| Female | 3 | 114 | 117 |
| Total | 15 | 200 | 215 |
Answer (1)
Calculate the total number of males: 12 + 86 = 98 .
Calculate the total number of females: 200 − 98 = 102 .
Calculate the number of females 'Under 6': 102 − 3 = 99 .
The correct two-way frequency table is A, which matches all calculated marginal frequencies: A .
Explanation
Analyze the problem and data We are given a two-way frequency table representing the heights of 200 adults, categorized by gender (Male, Female) and height (
Calculate the total number of males First, let's calculate the total number of males. From the table, we have 12 males who are '6 or over' and 86 males who are 'Under 6'. So, the total number of males is: 12 + 86 = 98
Calculate the total number of females Since there are 200 adults in total, the total number of females is: 200 − 98 = 102
Calculate the number of females 'Under 6' Now, let's find the number of females who are 'Under 6'. We know that there are 102 females in total, and 3 of them are '6 or over'. So, the number of females 'Under 6' is: 102 − 3 = 99
Calculate the total number of adults '6 or over' Next, let's calculate the total number of adults who are '6 or over'. We have 12 males and 3 females in this category. So, the total is: 12 + 3 = 15
Calculate the total number of adults 'Under 6' Finally, let's calculate the total number of adults who are 'Under 6'. We have 86 males and 99 females in this category. So, the total is: 86 + 99 = 185
Find the matching table Now, we need to find the table that matches our calculations. We are looking for a table with the following marginal frequencies:
Male: 98
Female: 102
'6 or over': 15
'Under 6': 185
Comparing our results with the given options, we find that option A matches our calculations.
Conclusion Therefore, the correct two-way frequency table is option A.
Examples
Two-way frequency tables are commonly used in market research to analyze customer demographics and preferences. For example, a company might use a two-way table to understand the relationship between age groups and product preferences. This helps them tailor their marketing strategies to specific customer segments, optimizing their advertising spend and increasing sales. Understanding how to calculate marginal frequencies is crucial for interpreting these tables and making informed business decisions.
