Question

using two-way tables to understand data
partial results of a survey about students who wear glasses are shown in the two-way table.

	wear glasses	wear glasses	wear glasses	wear glasses
boys	25	50
girls			48	98
total	60		100

which of the following statements are true? check all that apply.

• ☐ 225 students were surveyed.
• ☐ 25 girls always wear glasses.
• ☐ 15 girls sometimes wear glasses.
• ☐ 52 boys never wear glasses.
• ☐ 75 boys were surveyed.
• ☐ 65 students sometimes wear glasses.

Explanation:

Step1: Analyze "225 students were surveyed"

First, find the number of boys never wear glasses: Total never is 100, girls never is 48, so boys never = \(100 - 48 = 52\). Then find total boys: \(25 + 50 + 52 = 127\). Total girls is 98. Total surveyed = \(127 + 98 = 225\). So this is true.

Step2: Analyze "25 girls always wear glasses"

Total always is 60, boys always is 25, so girls always = \(60 - 25 = 35\). So this is false.

Step3: Analyze "15 girls sometimes wear glasses"

Total sometimes: First, total boys sometimes is 50, let girls sometimes be \(x\). Total sometimes = \(50 + x\). But we can find girls' always (35), never (48), so girls' sometimes = \(98 - 35 - 48 = 15\). So this is true.

Step4: Analyze "52 boys never wear glasses"

As calculated in Step1, boys never = \(100 - 48 = 52\). So this is true.

Step5: Analyze "75 boys were surveyed"

Total boys = \(25 + 50 + 52 = 127
eq75\). So this is false.

Step6: Analyze "65 students sometimes wear glasses"

Boys sometimes: 50, girls sometimes: 15 (from Step3). Total sometimes = \(50 + 15 = 65\). So this is true.

Answer:

• 225 students were surveyed. (True)
• 25 girls always wear glasses. (False)
• 15 girls sometimes wear glasses. (True)
• 52 boys never wear glasses. (True)
• 75 boys were surveyed. (False)
• 65 students sometimes wear glasses. (True)

The true statements are: "225 students were surveyed.", "15 girls sometimes wear glasses.", "52 boys never wear glasses.", "65 students sometimes wear glasses."