The mean is the average of a group of numbers. It tells us what each person or item would get if everything was shared equally.
How to Find the Mean – Step-by-Step
Step 1: Add all the numbers together.
Step 2: Count how many numbers there are.
Step 3: Divide the total by the number of values.
Mean= Sum of all values ÷ Number of values
Example:
Data: 10, 15, 20, 25, 30
Step 1: 10 + 15 + 20 + 25 + 30 = 100
Step 2: There are 5 numbers
Step 3: 100 ÷ 5 = 20 The mean is 20
Where is Mean Used?
In school to calculate average test scores
In sports to find average goals or points
In finance to calculate average spending or income
In science to find the average result from experiments
What is an Outlier?
An outlier is a number in a data set that is much higher or much lower than the other numbers. It doesn’t fit with the rest of the data and can affect the mean (average).
Example:
Data: 5, 6, 7, 6, 100
Most numbers are close to each other (5–7)
But 100 is much larger than the rest 100 is an outlier
Why Are Outliers Important?
They can change the mean a lot
They can show something unusual or special (like a mistake or surprise result)
In real life, they help scientists, teachers, and business people spot problems or interesting patterns
Questions
Criterion A: Knowledge and Understanding – Mean
1. Basic Mean Calculation
Find the mean of the following numbers: 8, 12, 15, 20, 25.
2. Mean of Test Scores
A student received the following scores on five quizzes: 78, 85, 90, 82, and 88. What is the average score?
3. Mean of Temperatures
The temperatures recorded over six days were: 18°C, 21°C, 19°C, 22°C, 20°C, and 23°C. Find the mean temperature for the six days.
4. Mean of Weekly Steps
A person walked the following number of steps each day: 5,200, 6,500, 7,800, 4,900, and 6,100. What is their average number of steps per day?
5. Finding the Missing Number
The mean of five numbers is 30. The first four numbers are 28, 35, 25, and 32. What is the missing number?
6. Mean of Distances Traveled
A car traveled the following distances over five days: 45 km, 50 km, 55 km, 40 km, and 60 km. Find the mean distance traveled per day.
Criterion D: Real-Life Problems on Mean
1. Test Scores and Performance
A student received the following scores in five science tests: 72, 85, 90, 78, and 95.
a) What is the student’s average score? b) If they want an average of at least 85, what score do they need on their next test? c) Does the mean always reflect the student’s performance accurately? Why or why not?
2. Daily Step Count and Fitness
A person records the number of steps they take over a week: 6,000, 8,500, 7,200, 9,300, 10,000, 12,500, and 5,800.
a) What is the average number of steps per day? b) If the goal is to walk at least 8,000 steps per day, did they meet their target on average? c) If one of the days was a mistake and the actual steps were 4,000 instead of 12,500, how would the mean change?
3. Sports Performance in Basketball
A basketball player scores the following points in six games: 15, 20, 25, 12, 18, and 30.
a) What is the player’s average points per game? b) If they score 40 points in their next game, how does the average change? c) Can one very high or very low score significantly affect the average? Explain why.
4. Class Attendance and Participation
A teacher records the number of students attending an after-school club each day for five days: 20, 22, 18, 25, and 30.
a) What is the average attendance per day? b) If attendance drops to 10 students on the sixth day, how does the average change? c) Is the mean always the best measure to describe attendance trends? What other data might be useful?
5. Weekly Grocery Expenses
A family spends the following amounts on groceries over five weeks: $120, $150, $130, $140, and $160.
a) What is the average amount spent per week? b) If they save $50 next week, how does the average change? c) Why might the mean not be the best way to analyze grocery spending? What other factors should be considered?
6. Temperature and Climate
The recorded temperatures in a city over seven days were: 25°C, 27°C, 22°C, 28°C, 30°C, 24°C, and 26°C.
a) What is the average temperature for the week? b) If one of the days was recorded incorrectly and the actual temperature was 35°C instead of 22°C, how does this affect the mean? c) Why might median or mode be better than mean in describing temperature trends?
7. Examining Average Speed in Travel
A bus travels the following distances over six trips: 45 km, 50 km, 48 km, 60 km, 52 km, and 55 km.
a) What is the average distance traveled per trip? b) If the bus only travels 30 km on its next trip, how does the average change? c) Why might the mean not always give the best picture of a bus’s typical travel distance?
Total of five numbers = 30 × 5 = 150 Sum of first four numbers = 28 + 35 + 25 + 32 = 120 Missing number = 150 – 120 = 30
6. Mean of Distances Traveled
Mean = (45 + 50 + 55 + 40 + 60) ÷ 5 = 50 km
Criterion D: Real-Life Problems on Mean
Answers
1. Test Scores and Performance
a) 84 b) 98 c) The mean gives an overall idea but does not show consistency. A single very high or very low score can affect the mean significantly.
2. Daily Step Count and Fitness
a) 8,757 steps per day b) Yes, the average is above 8,000. c) The new mean would drop significantly because 12,500 was a high value affecting the mean.
3. Sports Performance in Basketball
a) 20 points per game b) The new mean would be 22.14 points per game. c) Yes, one extreme value can raise or lower the mean significantly.
4. Class Attendance and Participation
a) 23 students per day b) The new mean would drop significantly because 10 is much lower than the other values. c) The median may be a better measure if attendance varies widely from day to day.
5. Weekly Grocery Expenses
a) $140 per week b) The new mean would be $131.67 per week. c) Some weeks may have higher or lower spending due to special events or discounts, making the median or mode useful as well.
6. Temperature and Climate
a) 26°C b) The new mean would increase due to 35°C being significantly higher. c) Median or mode may be better because extreme temperatures (like heat waves) can distort the mean.
7. Examining Average Speed in Travel
a) 51.67 km per trip b) The new mean would decrease significantly due to the 30 km trip. c) The mean may not represent usual distances if there is one very short or very long trip. The mode or range might be more useful.
