If a bar chart shows 60% Category A, 25% Category B, and 15% Category C and the sample size is 200, what are the expected counts for A, B, and C?

If a bar chart shows 60% Category A, 25% Category B, and 15% Category C and the sample size is 200, what are the expected counts for A, B, and C?

• A. A=100, B=60, C=40
• B. A=110, B=55, C=35
• C. A=120, B=50, C=30
• D. A=130, B=45, C=25

Answer: (C)

Start with the idea of turning category shares into actual counts by using the total sample size. To get expected counts, multiply each percentage by the sample size. With 200 observations: - 60% of 200 is 0.60 × 200 = 120 - 25% of 200 is 0.25 × 200 = 50 - 15% of 200 is 0.15 × 200 = 30 These counts sum to 200, which checks out. So the expected counts are 120 for A, 50 for B, and 30 for C, matching the option that lists 120, 50, 30. Other options would correspond to different proportions and do not fit the given shares.

Start with the idea of turning category shares into actual counts by using the total sample size. To get expected counts, multiply each percentage by the sample size.

With 200 observations:

• 60% of 200 is 0.60 × 200 = 120

• 25% of 200 is 0.25 × 200 = 50

• 15% of 200 is 0.15 × 200 = 30

These counts sum to 200, which checks out. So the expected counts are 120 for A, 50 for B, and 30 for C, matching the option that lists 120, 50, 30. Other options would correspond to different proportions and do not fit the given shares.