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Answer :
To solve this problem, we need to determine the percentage of athletes who took more than 26 seconds to finish a 200 m race based on the provided frequency table.
Here’s a step-by-step explanation:
1. Understanding the Table:
- The table shows different time intervals and the number of athletes (frequency) who finished the race within those time intervals:
- Between 22 and 24 seconds: 3 athletes
- Between 24 and 26 seconds: 5 athletes
- Between 26 and 28 seconds: 8 athletes
- Between 28 and 30 seconds: 9 athletes
2. Calculate the Total Number of Athletes:
- We add up all the frequencies to find the total number of athletes.
[tex]\[
3 + 5 + 8 + 9 = 25 \text{ athletes}
\][/tex]
3. Determine Athletes Who Took More Than 26 Seconds:
- The number of athletes who took more than 26 seconds are those who finished the race between 26 and 28 seconds, and between 28 and 30 seconds. So, we add those frequencies:
[tex]\[
8 + 9 = 17 \text{ athletes}
\][/tex]
4. Calculate the Percentage:
- To find the percentage of athletes who took more than 26 seconds, we use the formula:
[tex]\[
\text{Percentage} = \left(\frac{\text{Number of athletes who took more than 26 seconds}}{\text{Total number of athletes}}\right) \times 100
\][/tex]
- Plugging the values:
[tex]\[
\text{Percentage} = \left(\frac{17}{25}\right) \times 100 = 68.0\%
\][/tex]
Thus, 68% of the athletes took more than 26 seconds to finish the race.
Here’s a step-by-step explanation:
1. Understanding the Table:
- The table shows different time intervals and the number of athletes (frequency) who finished the race within those time intervals:
- Between 22 and 24 seconds: 3 athletes
- Between 24 and 26 seconds: 5 athletes
- Between 26 and 28 seconds: 8 athletes
- Between 28 and 30 seconds: 9 athletes
2. Calculate the Total Number of Athletes:
- We add up all the frequencies to find the total number of athletes.
[tex]\[
3 + 5 + 8 + 9 = 25 \text{ athletes}
\][/tex]
3. Determine Athletes Who Took More Than 26 Seconds:
- The number of athletes who took more than 26 seconds are those who finished the race between 26 and 28 seconds, and between 28 and 30 seconds. So, we add those frequencies:
[tex]\[
8 + 9 = 17 \text{ athletes}
\][/tex]
4. Calculate the Percentage:
- To find the percentage of athletes who took more than 26 seconds, we use the formula:
[tex]\[
\text{Percentage} = \left(\frac{\text{Number of athletes who took more than 26 seconds}}{\text{Total number of athletes}}\right) \times 100
\][/tex]
- Plugging the values:
[tex]\[
\text{Percentage} = \left(\frac{17}{25}\right) \times 100 = 68.0\%
\][/tex]
Thus, 68% of the athletes took more than 26 seconds to finish the race.
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