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Twenty-five adults reported the amount of time each spent exercising during a particular week. The results are summarized in the graph as follows: 5 respondents reported exercising for less than 1 hour, 3 respondents reported exercising for at least 1 hour but less than 2, and so on.
Based on the given information, use the drop-down menus to most accurately complete the following statements.
| Text Component | Literal Content | Simple Interpretation |
|---|---|---|
| Study participants | Twenty-five adults reported the amount of time each spent exercising during a particular week | 25 adults tracked their total weekly exercise time |
| Data presentation introduction | The results are summarized in the graph as follows: | A summary of responses is shown visually |
| First interval example | 5 respondents reported exercising for less than 1 hour | 5 people exercised between 0 and 1 hour in the week |
| Second interval example | 3 respondents reported exercising for at least 1 hour but less than 2 | 3 people exercised between 1 and 2 hours in the week |
| Continuation phrase | and so on | The same structure applies to following hour intervals and their counts |
| Chart Component | What's Shown | Meaning |
|---|---|---|
| Chart type | Histogram with bars representing numbers of respondents per hour interval | Displays how many people fall into each 1-hour exercise range |
| X-axis | Hours (intervals from 0-1, 1-2, ..., up to 10-11) | Groups weekly exercise time into ranges |
| Y-axis | Number of respondents (marked from 0 to 5) | The count of people in each range (maximum per bar is 5) |
| Main clusters | Two peaks: 0-1 hours (5 people), 5-6 hours (5 people) | Most exercise either very little or moderately (5-6 hours/week) |
| Gaps in data | 0 respondents for 6-7 and 7-8 hours | No one exercises between 6 and 8 hours/week; a distinct separation in exercise habits |
| Outliers | 1 person each at 8-9 and 10-11 hours | Only two people report unusually high weekly exercise |
The dataset shows a clear split in exercise behavior. The majority of respondents (\(\frac{23}{25}\)) exercise between 0 and 6 hours per week, concentrated at the low (0-1 hours) and moderate (5-6 hours) ends, creating a bimodal pattern. Two participants report much higher exercise (8-9 hours and 10-11 hours), with an empty gap in the 6-8 hour range. This suggests most people are either low or moderate exercisers, with very few high exercisers and no 'in-between' cases. The minimum possible average is about 3.1 hours per week, but many respondents exercise less than 3 hours. The data highlights both a tendency toward minimal activity and a smaller group of regular exercisers, but a near total absence of people in the 6-8 hour range.
The least possible value for the mean of the numbers of hours of exercise reported for the week is [BLANK].
The number of respondents who exercised on average less than one-half hour per day during the week is between [BLANK], inclusive.
To minimize the mean weekly exercise hours, assume each respondent is at the lower bound of their interval. This results in a minimum possible mean of 3.12 hours. For the number of respondents averaging less than 0.5 hours daily (3.5 per week), a certain 10 and as many as 14 could qualify, so the range is 10 and 14.
The two questions are independent: the mean (question 1) involves summing minimum possible values across all respondents, while the count (question 2) involves determining a range of qualifying individuals. Solving one does not require information from the other.