To solve this question, we need to analyze the given data about the time people spent exercising and calculate the total number of people. Here is a step-by-step explanation:
1. Understand the Data:
- The time intervals (in minutes) and their corresponding frequencies are given in a table.
- The frequencies represent the number of people who exercised for the given time intervals.
2. Identify the Midpoints of the Intervals:
- For easier calculations, we'll use the midpoint of each interval. The midpoints can be calculated as follows:
- For \(0 < x \leq 10\), the midpoint is \(\frac{0+10}{2} = 5\) minutes.
- For \(10 < x \leq 20\), the midpoint is \(\frac{10+20}{2} = 15\) minutes.
- For \(20 < x \leq 30\), the midpoint is \(\frac{20+30}{2} = 25\) minutes.
- For \(30 < x \leq 40\), the midpoint is \(\frac{30+40}{2} = 35\) minutes.
- For \(40 < x \leq 50\), the midpoint is \(\frac{40+50}{2} = 45\) minutes.
- For \(50 < x \leq 60\), the midpoint is \(\frac{50+60}{2} = 55\) minutes.
3. Summarize the Data:
- Midpoints: \( [5, 15, 25, 35, 45, 55] \)
- Frequencies: \( [18, 14, 3, 16, 21, 7] \)
4. Calculate the Total Number of People:
- The total number of people is the sum of all the frequencies.
[tex]\[
\begin{aligned}
\text{Total number of people} & = 18 + 14 + 3 + 16 + 21 + 7 \\
& = 79
\end{aligned}
\][/tex]
5. Solution Summary:
- We found the midpoints of each interval: \([5, 15, 25, 35, 45, 55]\).
- The frequencies are given as: \([18, 14, 3, 16, 21, 7]\).
- The total number of people who exercised is 79.
Therefore, the detailed results are the midpoints of the intervals, the frequencies, and the total number of people, which are:
[tex]\[
([5, 15, 25, 35, 45, 55], [18, 14, 3, 16, 21, 7], 79)
\][/tex]
