Frequency Tables

Show your work for each problem.

1.
What does "frequency" mean in a frequency table?
1. a)The average of all values
2. b)The largest value
3. c)The value itself
4. d)How many times a value appears
Answer: How many times a value appears
Frequency means how many times a value appears in the data set. It's a count, not the value itself.
2.
In a frequency table, the values Red: 5, Blue: 8, Green: 3 are listed. What is the total frequency?
1. a)8
2. b)24
3. c)3
4. d)16
Answer: 16
Total frequency = . This means there are 16 data points in total.
3.
A frequency table shows: A: 4, B: 7, C: 9. What is the total number of data points?
Answer: 20
Total data points = . The sum of frequencies equals the total number of data collected.
4.
What do four tally marks crossed by a fifth line represent? (||||)
Answer: 5
|||| equals 5. Four vertical marks plus one diagonal line crossing them makes counting by fives easy.
5.
Which category has the highest frequency? | Animal | Frequency | |--------|----------| | Dog | 12 | | Cat | 8 | | Bird | 15 | | Fish | 5 |
1. a)Cat
2. b)Fish
3. c)Dog
4. d)Bird
Answer: Bird
Bird has the highest frequency with 15. This means Bird was chosen most often.
6.
Students were asked their favorite sport. The results: Soccer appeared 8 times, Basketball 5 times, Tennis 3 times, Swimming 4 times. How many students were surveyed?
Answer: 20
Total students = . Each response counts as one student.
7.
A grouped frequency table has intervals 0-9, 10-19, 20-29. In which interval does the value 19 belong?
1. a)10-19
2. b)0-9
3. c)None of these
4. d)20-29
Answer: 10-19
The value 19 belongs in the interval 10-19 because 19 falls within this range (10 ≤ 19 ≤ 19).
8.
In a class survey, 12 students chose pizza, 8 chose burgers, and 5 chose salad. What fraction of students chose pizza? Write as a simplified fraction (e.g., 1/2).
Answer: 12/25
Total = . Pizza fraction = . This cannot be simplified further.
9.
Create a frequency table for this data: A, B, A, C, B, A, A, C, B, A. What is the frequency of each letter?
Answer: A:5, B:3, C:2
1. How many times does A appear? 5
2. How many times does B appear? 3
3. How many times does C appear? 2
4. What is the total? (Add all frequencies) 10
10.
The ages of people at a party are: 12, 15, 18, 12, 20, 15, 12, 18, 15, 12. Find the mode (most frequent value).
Answer: 12
1. How many times does 12 appear? 4
2. How many times does 15 appear? 3
3. How many times does 18 appear? 2
4. Which age appears most often? 12
11.
A student made a frequency table but the frequencies sum to 28, while they collected 30 data points. What mistake did they likely make?
1. a)Used wrong intervals
2. b)Counted some values twice
3. c)Made an addition error
4. d)Missed counting 2 data points
Answer: Missed counting 2 data points
Since , they missed 2 data points. The frequencies should always equal the total number of data collected.
12.
Group this data into intervals of 10 (10-19, 20-29, 30-39): 15, 22, 35, 18, 28, 31, 24, 19, 33, 26. Find the frequency for each interval.
Answer: 10-19:3, 20-29:4, 30-39:3
1. How many values fall in 10-19? (15, 18, 19) 3
2. How many values fall in 20-29? (22, 28, 24, 26) 4
3. How many values fall in 30-39? (35, 31, 33) 3
4. Verify: What is ? 10
13.
A store sold shoes in these sizes: 7, 8, 9, 8, 7, 10, 8, 9, 8, 7, 9, 8, 10, 8, 7. What is the relative frequency of size 8? (Write as a decimal, e.g., 0.25)
Answer: 0.4
Size 8 appears 6 times out of 15 total. Relative frequency = or 40%.
14.
A survey asked 50 people their favorite season. Spring: 12, Summer: 18, Fall: 15, Winter: ?. Find the frequency for Winter and the percentage who prefer Summer.
Answer: Winter: 5, Summer: 36%
1. What is ? 45
2. Winter frequency = = ? 5
3. Summer percentage = = ? 36
15.
Test scores: 72, 85, 91, 78, 85, 92, 88, 85, 79, 95, 85, 82. Create a grouped frequency table using intervals 70-79, 80-89, 90-99. Which interval has the highest frequency?
Answer: 80-89
1. How many scores are in 70-79? (72, 78, 79) 3
2. How many scores are in 80-89? (85, 85, 88, 85, 85, 82) 6
3. How many scores are in 90-99? (91, 92, 95) 3
4. Which interval has the highest frequency? 80-89
16.
Two classes took a test. Class A: mean score 75, 25 students. Class B: mean score 80, 15 students. If you combine the data, what is the total number of students?
Answer: 40
Total students = Class A + Class B = students. The mean scores are not needed for this calculation.