Question

question 5 of 10

the heights of 200 adults were recorded and divided into two categories.

which two-way frequency table correctly shows the marginal frequencies?

a.
b.
c.
d.

Explanation:

Identify given values

We are given the heights of 200 adults divided into categories:

• Total adults: \(200\)
• Males \(6'\) or over: \(12\)
• Males under \(6'\): \(86\)
• Females \(6'\) or over: \(3\)

Calculate missing values

Let \(x\) be the number of females under \(6'\).
The sum of all four joint frequencies must equal the total of 200 adults:

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

$$101 + x = 200$$

$$x = 99$$

Calculate marginal frequencies

Now we calculate the row and column totals (marginal frequencies):

• Total Males: \(12 + 86 = 98\)
• Total Females: \(3 + 99 = 102\)
• Total \(6'\) or over: \(12 + 3 = 15\)
• Total Under \(6'\): \(86 + 99 = 185\)
• Grand Total: \(98 + 102 = 200\) (or \(15 + 185 = 200\))

Match with options

Let's check the options for the correct values:

• Option A: Total is 298 (Incorrect).
• Option B: Total is 215 (Incorrect).
• Option C:
• Male row: \(12\) (\(6'\) or over), \(86\) (Under \(6'\)), Total = \(100\) (Incorrect, \(12 + 86 = 98\)).
• Option D (partially cut off but let's reconstruct the values):
• Male row: \(12\), \(86\), Total = \(98\).
• Female row: \(3\), \(99\), Total = \(102\).
• Total row: \(15\), \(185\), Total = \(200\).

Let's double check the visible parts of Option D:

• Male row: \(12\), \(86\), Total = \(98\).

This matches our calculated values. Thus, Option D is the correct table.

Answer:

• (A) Table with grand total 298
• (B) Table with grand total 215
• (C) Table with incorrect male total of 100
• (D) Table with correct marginal frequencies (grand total 200, male total 98, female total 102) (Correct answer)