Question

will surveyed students at his school about whether they have ever gone snowboarding and whether they own a skateboard. he found that 35 of the 99 students who own a skateboard have snowboarded. also, there were 13 students who have snowboarded but do not own a skateboard, and 147 students who have never gone snowboarding and do not own a skateboard.

which two-way table correctly displays this data?

Explanation:

Analyze the given data

We are given the following information from the survey:

• "35 of the 99 students who own a skateboard have snowboarded."
• This means the total number of students who own a skateboard is \(99\).
• Out of these, the number of students who own a skateboard and have snowboarded is \(35\).
• Consequently, the number of students who own a skateboard and have never snowboarded is:

$$ 99 - 35 = 64 $$

• "there were 13 students who have snowboarded but do not own a skateboard."
• This means the number of students in the "No Skateboard" and "Have Snowboarded" category is \(13\).

• "147 students who have never gone snowboarding and do not own a skateboard."
• This means the number of students in the "No Skateboard" and "Never Snowboarded" category is \(147\).

Determine the table values

Using the Two-Way Frequency Tables concept, we construct the cells:

• Skateboard / Have Snowboarded: \(35\)
• Skateboard / Never Snowboarded: \(64\)
• Skateboard Total: \(35 + 64 = 99\)
• No Skateboard / Have Snowboarded: \(13\)
• No Skateboard / Never Snowboarded: \(147\)
• No Skateboard Total: \(13 + 147 = 160\)

Calculate column totals

Now we calculate the totals for each column:

• Have Snowboarded Total:

$$ 35 + 13 = 48 $$

• Never Snowboarded Total:

$$ 64 + 147 = 211 $$

• Grand Total:

$$ 99 + 160 = 259 \quad (\text{or } 48 + 211 = 259) $$

Compare with the given options

Let's examine the third option shown in the image (partially visible at the bottom):

• Row 1 (Skateboard): Have Snowboarded = \(35\), Never Snowboarded = \(64\), Total = \(99\).
• Row 2 (No Skateboard): Have Snowboarded = \(13\), Never Snowboarded = \(147\), Total = \(160\).

This matches our derived values perfectly.

Answer:

• (A) Table with Skateboard Total = 48, No Skateboard Total = 211
• (B) Table with Skateboard Total = 134, No Skateboard Total = 160
• (C) Table with Skateboard Total = 99 (35 Have Snowboarded, 64 Never Snowboarded) and No Skateboard Total = 160 (13 Have Snowboarded, 147 Never Snowboarded) (Correct answer)