Mean (Average)
Test Scores
A student scored $85$, $92$, $78$, $88$, and $92$ on five tests. What is the mean score?
Add all the scores: $85 + 92 + 78 + 88 + 92 = 435$ = Sum = $435$
Count how many scores: There are $5$ test scores = Count = $5$
Divide the sum by the count: $\frac{435}{5} = 87$ = Mean = $87$
Answer: The mean test score is $87$.
Basketball Points
A player scored $12$, $18$, $15$, $22$, $8$, and $15$ points in six games. Find the mean points per game.
Add all the points: $12 + 18 + 15 + 22 + 8 + 15 = 90$ = Sum = $90$
Count the number of games: There are $6$ games = Count = $6$
Divide sum by count: $\frac{90}{6} = 15$ = Mean = $15$
Answer: The mean is $15$ points per game.
Finding a Missing Value
Four friends have a mean height of $150$ cm. Three of them are $145$ cm, $155$ cm, and $148$ cm tall. How tall is the fourth friend?
Find the total sum needed: Mean $\times$ Count = Total $150 \times 4 = 600$ cm = Total needed = $600$ cm
Add the known heights: $145 + 155 + 148 = 448$ cm = Known sum = $448$ cm
Subtract to find the missing height: $600 - 448 = 152$ cm = Missing height = $152$ cm
Answer: The fourth friend is $152$ cm tall.
Dealing with Decimals
The temperatures for a week were $18.5$, $21.2$, $19.8$, $22.1$, and $20.4$ degrees Celsius. What was the mean temperature?
Add all temperatures: $18.5 + 21.2 + 19.8 + 22.1 + 20.4 = 102$ = Sum = $102$
Count the days: There are $5$ days = Count = $5$
Divide to find the mean: $\frac{102}{5} = 20.4$ = Mean = $20.4$
Answer: The mean temperature was $20.4°C$.
Mistake: Forgetting to count all values
Why: When adding a long list of numbers, it's easy to miss one or count incorrectly.
Correct: Always count your values before dividing. Write them out and number them: 1st, 2nd, 3rd...
Mistake: Dividing by the sum instead of the count
Why: Confusing the formula - the divisor should be how many values you have, not their total.
Correct: Remember: Mean = Sum ÷ Count (how many numbers you added)
Mistake: Thinking the mean must be one of the original values
Why: The mean is a calculated value and often falls between the numbers in your data set.
Correct: The mean of $4$ and $10$ is $7$, which is not in the original data set - and that's okay!
Grade Point Average
Schools calculate your GPA by finding the mean of your grades, often weighted by credits.
If you earned $90$, $85$, $92$, and $88$ in four subjects, your mean grade is $\frac{90+85+92+88}{4} = 88.75$.
Sports Statistics
Athletes and teams track performance using averages - batting average, points per game, goals per match.
A soccer player scored $2$, $0$, $1$, $3$, $1$ goals in 5 matches. Mean = $\frac{7}{5} = 1.4$ goals per game.
The **mean** is found by adding all values and dividing by the count: $\text{Mean} = \frac{\text{Sum}}{\text{Count}}$
The mean represents a "typical" or "central" value in your data
The mean can be a decimal, even if all original values are whole numbers
To find a missing value when you know the mean: multiply mean by count, then subtract the known values
Q: What's the difference between mean and average?
A: They're the same thing! "Average" is the everyday word, while "mean" (specifically "arithmetic mean") is the mathematical term.
Q: Can the mean be higher than all the numbers?
A: No. The mean always falls between the smallest and largest values in your data set (or equals them if all values are the same).
Q: When should I NOT use the mean?
A: The mean can be misleading when you have extreme values (outliers). For example, if 5 people earn 30,000 dollars and 1 person earns 1,000,000 dollars, the mean salary would be misleadingly high.
Mean (Average)
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Mean (Average)
Learn how to calculate the mean of a data set by adding all values and dividing by the count.