Answer :
Sure, let's work through this question step by step:
a. What is the class width?
The class width is the difference between the upper and lower boundaries of any class. Looking at the intervals, for example, from 90-99, you subtract 90 from 99, which gives a class width of 9, but typically, class width is calculated as 10 because the intervals cover 10 numbers (e.g., 90 to 99 is 10 numbers: 90, 91, 92, 93, 94, 95, 96, 97, 98, 99).
Answer: c. 10
b. What is the total number of visitors?
To find the total number of visitors, you add up the frequencies from all the classes.
- 1 (from 90-99)
- 4 (from 100-109)
- 4 (from 110-119)
- 3 (from 120-129)
- 7 (from 130-139)
- 6 (from 140-149)
- 4 (from 150-159)
- 2 (from 160-169)
Total = 1 + 4 + 4 + 3 + 7 + 6 + 4 + 2 = 31
Answer: 31
c. Compute the relative frequencies.
Relative frequency is the frequency of each class divided by the total number of observations. Here's how you compute it for each class:
- For 90-99: [tex]\( \frac{1}{31} \approx 0.0323 \)[/tex]
- For 100-109: [tex]\( \frac{4}{31} \approx 0.1290 \)[/tex]
- For 110-119: [tex]\( \frac{4}{31} \approx 0.1290 \)[/tex]
- For 120-129: [tex]\( \frac{3}{31} \approx 0.0968 \)[/tex]
- For 130-139: [tex]\( \frac{7}{31} \approx 0.2258 \)[/tex]
- For 140-149: [tex]\( \frac{6}{31} \approx 0.1935 \)[/tex]
- For 150-159: [tex]\( \frac{4}{31} \approx 0.1290 \)[/tex]
- For 160-169: [tex]\( \frac{2}{31} \approx 0.0645 \)[/tex]
d. How many visitors are below 129 lbs?
To find how many visitors are below 129 lbs, add up the frequencies for the classes from 90-99 through 120-129.
- Visitors below 129 lbs: 1 + 4 + 4 + 3 = 12
Answer: 12
e. What is the complement of less than 159 lbs?
First, find how many visitors are less than 159 lbs by summing the frequencies from classes 90-99 up to 150-159.
- Visitors less than 159 lbs: 1 + 4 + 4 + 3 + 7 + 6 + 4 = 29
The complement is the total number of visitors minus those who are less than 159 lbs.
- Complement = Total visitors - Visitors less than 159 lbs = 31 - 29 = 2
Answer: 2
I hope this helps! Let me know if you have any more questions.
a. What is the class width?
The class width is the difference between the upper and lower boundaries of any class. Looking at the intervals, for example, from 90-99, you subtract 90 from 99, which gives a class width of 9, but typically, class width is calculated as 10 because the intervals cover 10 numbers (e.g., 90 to 99 is 10 numbers: 90, 91, 92, 93, 94, 95, 96, 97, 98, 99).
Answer: c. 10
b. What is the total number of visitors?
To find the total number of visitors, you add up the frequencies from all the classes.
- 1 (from 90-99)
- 4 (from 100-109)
- 4 (from 110-119)
- 3 (from 120-129)
- 7 (from 130-139)
- 6 (from 140-149)
- 4 (from 150-159)
- 2 (from 160-169)
Total = 1 + 4 + 4 + 3 + 7 + 6 + 4 + 2 = 31
Answer: 31
c. Compute the relative frequencies.
Relative frequency is the frequency of each class divided by the total number of observations. Here's how you compute it for each class:
- For 90-99: [tex]\( \frac{1}{31} \approx 0.0323 \)[/tex]
- For 100-109: [tex]\( \frac{4}{31} \approx 0.1290 \)[/tex]
- For 110-119: [tex]\( \frac{4}{31} \approx 0.1290 \)[/tex]
- For 120-129: [tex]\( \frac{3}{31} \approx 0.0968 \)[/tex]
- For 130-139: [tex]\( \frac{7}{31} \approx 0.2258 \)[/tex]
- For 140-149: [tex]\( \frac{6}{31} \approx 0.1935 \)[/tex]
- For 150-159: [tex]\( \frac{4}{31} \approx 0.1290 \)[/tex]
- For 160-169: [tex]\( \frac{2}{31} \approx 0.0645 \)[/tex]
d. How many visitors are below 129 lbs?
To find how many visitors are below 129 lbs, add up the frequencies for the classes from 90-99 through 120-129.
- Visitors below 129 lbs: 1 + 4 + 4 + 3 = 12
Answer: 12
e. What is the complement of less than 159 lbs?
First, find how many visitors are less than 159 lbs by summing the frequencies from classes 90-99 up to 150-159.
- Visitors less than 159 lbs: 1 + 4 + 4 + 3 + 7 + 6 + 4 = 29
The complement is the total number of visitors minus those who are less than 159 lbs.
- Complement = Total visitors - Visitors less than 159 lbs = 31 - 29 = 2
Answer: 2
I hope this helps! Let me know if you have any more questions.
