To answer the questions about relative frequency, let’s analyze the histogram and the frequency of each interval:

1. Determine Total Frequency: We need to sum up the frequency counts for each interval shown on the histogram:

   • $67-74$: 4
   • $75-82$: 5
   • $83-90$: 7
   • $91-98$: 3
   • $99-106$: 2

   Total frequency = $4 + 5 + 7 + 3 + 2 = 21$

2. Relative Frequency Calculations:

   • Part (a): Relative frequency for scores $75-82$: $\text{Relative frequency} = \frac{\text{Frequency of } 75-82}{\text{Total frequency}} = \frac{5}{21} \approx 0.238$

   • Part (b): Relative frequency for scores $91-106$: Since $91-98$ has a frequency of 3 and $99-106$ has a frequency of 2, we combine these for the range $91-106$. $\text{Relative frequency} = \frac{\text{Frequency of } 91-98 + \text{Frequency of } 99-106}{\text{Total frequency}} = \frac{3 + 2}{21} = \frac{5}{21} \approx 0.238$

Answers:

• (a): The relative frequency of scores $75-82$ is approximately 0.238.
• (b): The relative frequency of scores $91-106$ is approximately 0.238.

Would you like further explanation or additional help with similar questions?

Related Questions:

1. What is the relative frequency of scores in the interval $67-74$?
2. How do you calculate cumulative frequency based on a histogram?
3. What is the probability of randomly selecting a participant with a score in the $83-90$ range?
4. How can you represent the data in a cumulative frequency chart?
5. How is relative frequency helpful in interpreting data distributions?

Tip:

In a histogram, relative frequency provides insight into the proportion of data within each interval, which can be useful for comparing data without considering sample size.