MYP1 Mathematics

About Lesson

The mode is the number (or item) that appears most frequently in a data set. Here are some important rules to remember:

Rule 1: A Data Set Can Have One Mode (Unimodal)

If only one number appears the most, that number is the mode.
Example: 3, 4, 5, 3, 6, 7, 3 → The mode is 3 because it appears the most.

Rule 2: A Data Set Can Have More Than One Mode (Bimodal or Multimodal)

If two numbers appear the most (with the same frequency), the set is bimodal (two modes).
If three or more numbers appear most frequently, it is multimodal.
Example (Bimodal): 2, 5, 6, 2, 7, 6, 8 → Modes are 2 and 6.
Example (Multimodal): 1, 3, 4, 1, 3, 4, 6 → Modes are 1, 3, and 4.

Rule 3: If No Number Repeats, There is No Mode

If all numbers appear only once, then the data has no mode.
Example: 2, 5, 8, 11, 14 → No mode because no number repeats.

Rule 4: The Mode Can Be Used for Non-Numerical Data

Mode is not just for numbers! It works with words, colors, or choices.
Example: If students vote for their favorite color:
- Red, Blue, Blue, Green, Red, Blue → Mode = Blue (appears most).

Rule 5: The Mode is Useful for Identifying Popular Trends

The mode helps find the most common choice in surveys, sales, voting, and business trends.

Criterion D: Real-Life Problems on Mode

1. Mode of Daily Step Count

A fitness tracker records the following step counts over a week: 6,500, 7,200, 7,200, 6,800, 6,500, 7,500, and 7,200.

a) What is the mode of the step counts?
b) If a person wants to increase their daily steps, how useful is knowing the mode?
c) Is the mode always the best measure to analyze step counts? Why or why not?

2. Mode of Test Scores

A math teacher recorded students’ test scores: 85, 90, 92, 85, 95, 88, 85, 90, 95, 92.

a) What is the mode of the test scores?
b) What does the mode tell us about student performance?
c) If one student retakes the test and scores 85, how does this affect the mode?

3. Most Popular Shoe Size

The shoe sizes of students in a sports team are: 38, 40, 41, 40, 39, 40, 38, 41, 40, 39.

a) Find the mode of the shoe sizes.
b) How does knowing the mode help a store owner who wants to stock shoes for students?
c) Would the mean or median be useful in this case? Why or why not?

4. Common Favorite Ice Cream Flavor

A survey asked students about their favorite ice cream flavor. The results were: Chocolate, Vanilla, Strawberry, Chocolate, Mango, Vanilla, Chocolate, Chocolate, Mango, Vanilla.

a) What is the mode of the favorite ice cream flavors?
b) How can knowing the mode help an ice cream shop owner?
c) If a new student joins the survey and picks Mango, does it change the mode? Why or why not?

5. Mode of Monthly Rainfall Days

The number of days it rained each month in a year were: 10, 12, 8, 15, 12, 10, 12, 9, 12, 15, 8, 10.

a) Find the mode of the number of rainy days.
b) How can this information be useful for planning outdoor events?
c) Would the mean or mode be a better measure for predicting future rainfall? Explain.

6. Mode of Most Watched TV Channel

A group of friends recorded how many times they watched different TV channels in a week:
Sports: 4, News: 2, Movies: 5, Sports: 4, Cartoons: 6, Sports: 4, Movies: 5, Cartoons: 6.

a) What is the mode of the most-watched TV channels?
b) How can knowing the mode be useful for advertisers?
c) If one more person watches the News channel, will the mode change? Why or why not?

7. Mode of Classroom Attendance

A teacher recorded the number of students attending an after-school program each day for two weeks:
18, 20, 22, 18, 19, 21, 18, 20, 22, 20, 18, 19, 22, 18.

a) What is the mode of attendance?
b) How can this information help the teacher plan classroom activities?
c) Is the mode always the best measure for attendance trends? Why or why not?

Criterion A: Knowledge and Understanding – Mode

1. Finding the Mode

Find the mode of the following set of numbers: 3, 7, 7, 2, 5, 7, 4, 5, 2, 3.

2. Mode of Test Scores

A student took six quizzes and scored: 85, 90, 95, 85, 80, and 90.
What is the mode of their scores?

3. Mode of Daily Steps

A person recorded the number of steps taken each day: 6,200, 7,500, 6,200, 8,000, 7,500, 7,500, 6,200.
What is the mode of their step counts?

4. Mode of Shoe Sizes

The shoe sizes of students in a class are: 38, 40, 41, 40, 39, 40, 38, 41, 40, 39.
What is the mode of the shoe sizes?

5. Identifying No Mode

Find the mode of the following numbers: 12, 18, 25, 30, 35, 40.

6. Finding Multiple Modes

Find the mode of the set: 45, 50, 55, 45, 60, 55, 50, 45, 55, 60.

7. Mode of Test Results

A teacher records students’ scores in a spelling test: 10, 8, 9, 7, 10, 8, 9, 10, 9, 8.
What is the mode of the test scores?

Answers

Criterion D: Real-Life Problems on Mode

1. Mode of Daily Step Count

a) Mode = 7,200 steps
b) It helps identify the most common daily step count but does not show overall trends.
c) The mean might be more useful in tracking progress over time.

2. Mode of Test Scores

a) Mode = 85
b) It shows the most frequently occurring score.
c) The mode increases the importance of 85 as a common score, making it even more representative.

3. Most Popular Shoe Size

a) Mode = 40
b) It helps stores know which size to stock more of.
c) The mode is more useful than the mean because shoe sizes are discrete values, and averaging them may not make sense.

4. Common Favorite Ice Cream Flavor

a) Mode = Chocolate
b) It helps shop owners stock the most popular flavor.
c) The mode does not change because Chocolate is still the most frequently chosen.

5. Mode of Monthly Rainfall Days

a) Mode = 12 rainy days
b) It helps in planning outdoor events by showing the most common number of rainy days.
c) The mean might be better if rainfall varies widely between months.

6. Mode of Most Watched TV Channel

a) Mode = Sports (4 times)
b) It helps advertisers decide which channels to focus on.
c) The mode will not change unless News becomes more frequent than Sports.

7. Mode of Classroom Attendance

a) Mode = 18 students
b) It helps the teacher prepare for the most common number of students attending.
c) The mean might be more useful if attendance fluctuates a lot.

Criterion A: Knowledge and Understanding – Mode

Answers

1. Finding the Mode

Mode = 7 (appears 3 times)

2. Mode of Test Scores

Modes = 85 and 90 (both appear twice)

3. Mode of Daily Steps

Modes = 6,200 and 7,500 (both appear 3 times)

4. Mode of Shoe Sizes

Mode = 40 (appears 4 times)

5. Identifying No Mode

There is no mode (each number appears only once)

6. Finding Multiple Modes

Modes = 45 and 55 (both appear 3 times)

7. Mode of Test Results

Mode = 10, 8, and 9 (each appears 3 times)