Creating a Frequency Table from Raw Data

A teacher asked 20 students their favorite color. The responses were: Red, Blue, Blue, Green, Red, Blue, Yellow, Red, Green, Blue, Red, Blue, Yellow, Red, Green, Blue, Blue, Red, Yellow, Green. Create a frequency table.

List each unique value: The colors mentioned are: Red, Blue, Green, Yellow = 4 categories

Count Red: Red appears: positions 1, 5, 8, 11, 15, 18 = Red: 6

Count Blue: Blue appears: positions 2, 3, 6, 10, 12, 16, 17 = Blue: 7

Count Green: Green appears: positions 4, 9, 15, 20 = Green: 4

Count Yellow: Yellow appears: positions 7, 13, 19 = Yellow: 3

Verify the total: $6 + 7 + 4 + 3 = 20$ = Total matches!

Answer: | Color | Frequency | |-------|----------| | Red | 6 | | Blue | 7 | | Green | 4 | | Yellow | 3 | | **Total** | **20** |

Reading a Frequency Table

The table shows test scores for a class: | Score | Frequency | |-------|----------| | A | 5 | | B | 12 | | C | 8 | | D | 3 | | F | 2 | a) How many students are in the class? b) What was the most common grade? c) How many students passed (A, B, or C)?

Find total students: $5 + 12 + 8 + 3 + 2 = 30$ = 30 students

Find most common grade: B has the highest frequency (12) = B is most common

Count passing grades: A + B + C = $5 + 12 + 8 = 25$ = 25 students passed

Answer: a) 30 students b) B was most common c) 25 students passed

Frequency Table with Grouped Data

Students recorded how many minutes they spent on homework: 15, 22, 35, 18, 42, 28, 31, 19, 45, 25, 33, 20, 38, 27, 41, 24 Create a grouped frequency table using intervals of 10 minutes.

Determine the range: Minimum: 15, Maximum: 45 = Range: 15-45 minutes

Set up intervals: 10-19, 20-29, 30-39, 40-49 = 4 groups

Count 10-19: 15, 18, 19 are in this range = 3

Count 20-29: 22, 28, 25, 20, 27, 24 are in this range = 6

Count 30-39: 35, 31, 33, 38 are in this range = 4

Count 40-49: 42, 45, 41 are in this range = 3

Verify: $3 + 6 + 4 + 3 = 16$ data points = Correct!

Answer: | Minutes | Frequency | |---------|----------| | 10-19 | 3 | | 20-29 | 6 | | 30-39 | 4 | | 40-49 | 3 | | **Total** | **16** |

Mistake: Forgetting to check that frequencies sum to total data points

Why: If the sum doesn't match the number of data points, you've miscounted somewhere.

Correct: Always add up all frequencies and verify it equals the total number of data values collected.

Mistake: Missing a category when counting

Why: When scanning through data quickly, it's easy to skip values or count the same one twice.

Correct: Use tally marks and cross off each data point as you count it.

Mistake: Putting a data value in the wrong interval for grouped data

Why: The boundaries can be confusing. Is 20 in '10-20' or '20-30'?

Correct: Decide whether intervals include the left endpoint, right endpoint, or both. Be consistent!

Sports Statistics

Coaches use frequency tables to analyze player performance and game outcomes.

A basketball coach tracks the number of points scored by each player in 10 games to find the most consistent scorer.

Inventory Management

Stores track product sales using frequency tables to know what to reorder.

A shoe store counts how many pairs of each size sold this week to stock the most popular sizes.

Q: What's the difference between frequency and relative frequency?

A: Frequency is the count (like 5 students). Relative frequency is the proportion or percentage (like 25% of students). Relative frequency = frequency divided by total.

Q: When should I use grouped data instead of individual values?

A: Use grouped data when you have many different values (like ages from 1-100) or continuous data. It makes the table easier to read and reveals patterns.

Q: Do I always need tally marks in a frequency table?

A: No, tally marks are optional. They're useful while counting data, but the final table often shows just the frequency numbers.