Question

a sociologist looks at trends in flea-borne typhus cases among humans in a certain county. flea-borne typhus, human cases by year for the entire county, years 1–20 *at year 20, the current 5-year average was 99.6 cases per year, based on the data from years 16–20. adapted from http://publichealth.lacounty.gov/ which of the following is a false impression the graphic could create? a. the current 5-year average is based on a range of 8 to 137. b. the current 5-year average is based on a range of 67 to 137. c. the current 5-year average would have been lower at year 5. d. the current 5-year average is likely to increase after year 20.

Explanation:

Step1: Analyze Option A

The 5 - Year Average at Year 20 is based on Years 16 - 20. The values for these years are 67, 109, 93, 92, 137. The range of these values is from 67 to 137? No, wait, the minimum in 16 - 20 is 67? Wait, no, the values are 67 (Year 16), 109 (Year 17), 93 (Year 18), 92 (Year 19), 137 (Year 20). But the overall data from Year 1 - 20 has a range from 8 to 137. However, the 5 - Year Average at Year 20 is based on Years 16 - 20, not the entire range. But let's check the option: "The current 5 - Year Average is based on a range of 8 to 137." The 5 - Year Average at Year 20 is based on Years 16 - 20, so its range is from 67 to 137? Wait, no, the values in 16 - 20 are 67, 109, 93, 92, 137. The minimum here is 67, maximum 137. But the option A says range 8 - 137. 8 is from Year 3. But the 5 - Year Average at Year 20 is based on 16 - 20, so the data for the average is from 16 - 20, so the range of the data used for the 5 - Year Average at Year 20 is 67 - 137, not 8 - 137. Wait, maybe I misread. Wait, the question is about the false impression. Let's check each option:

Step2: Analyze Option B

The 5 - Year Average at Year 20 is based on Years 16 - 20. The values for these years are 67, 109, 93, 92, 137. The range of these values is 67 (minimum) to 137 (maximum), so this statement is true.

Step3: Analyze Option C

At Year 5, the 5 - Year Average would be based on Years 1 - 5. The values for Years 1 - 5 are 11, 12, 8, 9, 10. The average of these is \(\frac{11 + 12+8 + 9+10}{5}=\frac{50}{5} = 10\). At Year 20, the 5 - Year Average is 99.6. So the 5 - Year Average at Year 5 is lower than at Year 20, so the statement "The current 5 - Year Average would have been lower at Year 5" is true.

Step4: Analyze Option D

After Year 20, if the trend continues (the last value is 137, which is higher than the 5 - Year Average of 99.6), it is likely that the 5 - Year Average (which is a moving average) will increase as new years (after 20) with potentially high values (if the trend of increasing continues) are included. So this statement is a reasonable impression, not false.

Step5: Analyze Option A again

The 5 - Year Average at Year 20 is based on Years 16 - 20. The data for these years has a range from 67 (Year 16) to 137 (Year 20). But the option A says the range is 8 to 137. 8 is from Year 3, which is not in the 16 - 20 range. So the graph might give the false impression that the 5 - Year Average is based on a range of 8 to 137 (using the overall data range) when in fact, for the 5 - Year Average at Year 20, it's based on 16 - 20 with range 67 - 137. Wait, but let's check the option again. Wait, the question is which is a false impression. Wait, maybe I made a mistake. Wait, the 5 - Year Average line is a dashed line. The graph shows the number of cases (solid line) with values from 8 (Year 3) to 137 (Year 20). The 5 - Year Average at Year 20 is 99.6, based on 16 - 20. But the graph's solid line has a range from 8 to 137, and the 5 - Year Average line is around 100. So someone might think that the 5 - Year Average is based on the entire range (8 - 137) of the solid line's data, but it's actually based on 16 - 20. But let's check the options again. Wait, option A: "The current 5 - Year Average is based on a range of 8 to 137." The 5 - Year Average at Year 20 is based on 16 - 20, so the data for the average is 67, 109, 93, 92, 137. The range of these is 67 - 137, not 8 - 137. But option B: "The current 5 - Year Average is based on a range of 67 to 137." That's true. Option A is saying the range is 8 - 137, which is false because the 5 - Year Average at Year 20 is based on 16 - 20, not including 8. Wait, but maybe I messed up. Wait, let's re - evaluate.

Wait, the key is that the 5 - Year Average at Year 20 is calculated using the data from Years 16 - 20. The values in those years are 67, 109, 93, 92, 137. The range of these values is 67 (minimum) to 137 (maximum). Option A says the range is 8 to 137. 8 is a value from Year 3, which is not in the 16 - 20 range. So the graph might give the false impression that the 5 - Year Average is based on data with a range of 8 to 137 (using the lowest value in the entire dataset) when in fact, for the 5 - Year Average at Year 20, it's based on data with a range of 67 to 137. But wait, the question is which is a false impression. Wait, maybe I got the options wrong. Wait, let's check the options again:

Option A: The current 5 - Year Average is based on a range of 8 to 137.

Option B: The current 5 - Year Average is based on a range of 67 to 137.

Option C: The current 5 - Year Average would have been lower at Year 5.

Option D: The current 5 - Year Average is likely to increase after Year 20.

Wait, at Year 5, the 5 - Year Average would be based on Years 1 - 5: 11, 12, 8, 9, 10. The average is \(\frac{11 + 12+8 + 9+10}{5}=\frac{50}{5}=10\), which is lower than 99.6 at Year 20, so C is true.

For D, since Year 20 has 137 cases, which is higher than the 5 - Year Average of 99.6, if future years (after 20) have high cases (following the trend of Year 20), the 5 - Year Average (which is a moving average) will increase as we include these high - value years. So D is a reasonable impression.

Now, between A and B. The 5 - Year Average at Year 20 is based on Years 16 - 20. The data for these years: 67 (Year 16), 109 (Year 17), 93 (Year 18), 92 (Year 19), 137 (Year 20). The range of these values is 67 (min) to 137 (max), so B is true. A says the range is 8 to 137. 8 is from Year 3, which is not in the 16 - 20 range, so A is a false impression. Wait, but maybe I made a mistake. Wait, the question is which is a false impression. So the answer should be A? Wait, no, wait the option A: "The current 5 - Year Average is based on a range of 8 to 137." The 5 - Year Average is a moving average. At each year, it's based on the previous 5 years. At Year 20, it's based on 16 - 20. But the graph shows the solid line with values from 8 to 137, and the dashed line (5 - Year Average) is around 100. So someone might think that the 5 - Year Average is calculated using data from the entire range (8 - 137) of the solid line, but it's actually calculated using the last 5 years (16 - 20) with range 67 - 137. So A is a false impression. But wait, let's check the option again. Wait, maybe I got the options reversed. Wait, the correct answer is A? Wait, no, let's re - check.

Wait, the 5 - Year Average at Year 20 is based on Years 16 - 20. The values in those years are 67, 109, 93, 92, 137. The minimum of these is 67, maximum 137. So the range of the data used for the 5 - Year Average at Year 20 is 67 - 137. Option A says the range is 8 - 137, which is incorrect (since 8 is not in 16 - 20), so A is a false impression. Option B says the range is 67 - 137, which is correct. So the false impression is A. Wait, but the original question's options: let's check again.

Wait, the problem is asking which is a false impression. So the answer is A. But wait, maybe I made a mistake. Let's confirm:

- Option A: The current 5 - Year Average (at Year 20) is based on a range of 8 to 137. But the 5 - Year Average at Year 20 is based on Years 16 - 20, whose data has a range of 67 (Year 16) to 137 (Year 20), not 8 (Year 3) to 137. So this is a false impression.

- Option B: The current 5 - Year Average is based on a range of 67 to 137. This is true, as the data for Years 16 - 20 is 67, 109, 93, 92, 137, so range 67 - 137.

- Option C: The current 5 - Year Average would have been lower at Year 5. At Year 5, the 5 - Year Average is based on Years 1 - 5: 11, 12, 8, 9, 10. Average is \(\frac{11 + 12+8 + 9+10}{5}=10\), which is lower than 99.6 at Year 20, so this is true.

- Option D: The current 5 - Year Average is likely to increase after Year 20. Since Year 20 has 137 cases (higher than the 5 - Year Average of 99.6), if future years (after 20) have high cases (following the upward trend of Year 20), the 5 - Year Average (a moving average) will increase as we include these high - value years. So this is a reasonable (not false) impression.

So the false impression is Option A.

Answer:

A. The current 5 - Year Average is based on a range of 8 to 137.