Learn how to calculate the arithmetic mean (average) in 2 steps: add all values, divide by count. With 30 practice problems and mean vs median vs mode comparison.
Mean = sum of all values ÷ count. For 4,7,13,2,9: sum=35, count=5. Mean=35÷5=7. The mean should always fall between the minimum and maximum values.
| Measure | Best for | Avoid when |
|---|---|---|
| Mean | Symmetric data, test scores | Outliers present (salaries) |
| Median | Skewed data, income | Need exact mathematical average |
| Mode | Categories, sizes, surveys | All values are unique |
Exam 60% weight (score 75), homework 40% weight (score 90): mean=0.6×75+0.4×90=45+36=81. Not all averages are simple means.
5 people earn $20k each and 1 earns $200k. Mean=$53.3k — nobody earns that! Median=$20k is much more representative.
Yes. 1,2,3 has mean 2. But 1,2,4 has mean 7/3=2.333... The mean doesn't have to be one of the data values.
They're the same thing. 'Average' is the everyday word; 'mean' (specifically 'arithmetic mean') is the mathematical term. Both = sum÷count.
If you add k to every value, the mean also increases by k. If you multiply all values by k, the mean also multiplies by k.
| Situation | Use Mean | Use Median |
|---|---|---|
| Symmetric data | ✓ Best choice | Works too |
| Salaries (outliers) | ✗ Misleading | ✓ Better |
| Test scores | ✓ Standard | Optional |
| House prices | ✗ Skewed | ✓ Preferred |
9 workers earn $8,000 and the owner earns $90,000. Mean=$17,000 — nobody actually earns that. Median=$8,000 — accurate. The mean gets pulled toward extreme values.
A player with 3 hits in 10 at-bats has a .300 average (30%). That's the mean number of hits per at-bat, multiplied by 10. Sports statistics are full of means.
Yes, and it often is. Mean of 1,2,4=2.33. The value 2.33 does not appear in the data. The mean is a mathematical construct, not necessarily an observed value.
Yes, by exactly that amount. If every value increases by k, the mean increases by k. If every value is multiplied by k, the mean is also multiplied by k.
Population mean (μ): calculated from all members. Sample mean (x̄): calculated from a subset. In statistics, we usually have sample means and use them to estimate μ.
Formula — Media Aritmetica
Media = (x1 + x2 + x3 + ... + xn) / n
Suma todos los datos y divide entre cuantos hay.
Ejemplo: {3,5,7,9,11} -> suma=35, n=5 -> media=7
Cuando NO usar la media
Si hay valores extremos, la media distorsiona. Ejemplo: sueldos $8k,$9k,$10k,$11k,$100k -> media=$27.6k pero nadie gana eso. En ese caso usar la mediana ($10k).
The mean (also called average or arithmetic mean) is the most commonly used measure of central tendency in statistics. It represents the "typical" value in a dataset. Learning how to find the mean is essential for math class, standardized tests, and everyday life.
Mean = Sum of all values ÷ Number of values
Step 1: Add all the numbers in your data set.
Step 2: Count how many numbers are in your data set.
Step 3: Divide the sum (Step 1) by the count (Step 2).
Step 4: The result is the mean.
Data: 4, 7, 13, 2, 9
Step 1: 4 + 7 + 13 + 2 + 9 = 35
Step 2: There are 5 numbers
Step 3: 35 ÷ 5 = 7
Mean = 7
A student got these scores: 85, 92, 78, 90, 88
Sum = 85 + 92 + 78 + 90 + 88 = 433
Count = 5 tests
Mean = 433 ÷ 5 = 86.6
The mean of 4 numbers is 10. Three numbers are 8, 11, 9. What is the fourth?
Total sum needed = 10 × 4 = 40
Sum of known numbers = 8 + 11 + 9 = 28
Missing number = 40 - 28 = 12
Mean: Sum ÷ count. Affected by extreme values (outliers).
Median: The middle value when data is ordered. Not affected by outliers.
Mode: The most frequent value. A dataset can have multiple modes or none.
Example: Data: 2, 3, 3, 7, 100
Mean = (2+3+3+7+100)/5 = 115/5 = 23 ← pulled high by outlier 100
Median = 3 ← middle value, not affected by 100
Mode = 3 ← appears most often
When some values are more important than others, use the weighted mean:
Weighted Mean = Σ(value × weight) ÷ Σ(weights)
Example: Final grade: Homework 20%, Midterm 30%, Final exam 50%
Scores: Homework 90, Midterm 80, Final 70
Weighted mean = (90×0.2 + 80×0.3 + 70×0.5) = 18 + 24 + 35 = 77
✅ Use the mean when: data is symmetric, no extreme outliers, interval or ratio data
❌ Avoid the mean when: there are extreme outliers (income distributions, house prices), data is skewed, ordinal or categorical data
1. Find the mean of 5, 8, 12, 15, 10 → (5+8+12+15+10)/5 = 50/5 = 10
2. Temperatures this week: 28, 31, 27, 30, 29, 33, 26 → 204/7 = 29.1°C
3. Mean of 0, 0, 0, 100 → 100/4 = 25 (outlier effect!)
4. 7 students: ages 12, 13, 12, 14, 13, 12, 15 → 91/7 = 13
5. Sales: $1200, $980, $1100, $1320 → 4600/4 = $1,150
6. Mean of 100, 200, 300 → 600/3 = 200
7. A class average is 75 with 20 students. Total points = 1,500
8. Heights: 160, 172, 168, 165, 175 cm → 840/5 = 168 cm
9. Mean of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 → 55/10 = 5.5
10. If 3 numbers average 8, their sum = 8×3 = 24
Los mejores matemáticos del mundo no memorizan fórmulas — entienden los conceptos detrás de ellas. Cuando entiendes POR QUÉ funciona una fórmula, nunca la olvidas. En cambio, si solo la memorizas sin entender, la olvidarás pronto.
Para cada problema de matemáticas, sigue este método: lee el problema completo, identifica qué datos tienes, identifica qué te piden encontrar, selecciona la fórmula o método adecuado, resuelve paso a paso, y verifica tu respuesta.
Este tema matemático aparece constantemente en situaciones cotidianas. Las matemáticas no son un tema abstracto que solo existe en los libros — son el lenguaje con el que describimos el mundo. Desde calcular el cambio en una tienda hasta diseñar un puente, desde predecir el clima hasta programar una aplicación, las matemáticas están en todo.
En México, las materias donde más necesitas estas habilidades son: física, química, economía, geografía y estadística. En el COMIPEMS, los temas de matemáticas representan una gran parte del examen.
El COMIPEMS incluye aproximadamente 128 preguntas de matemáticas distribuidas en aritmética, álgebra, geometría y estadística. Para maximizar tu puntaje:
Aritmética (40% del examen): Fracciones, decimales, porcentajes, potencias, raíces. Practica operaciones sin calculadora.
Álgebra (25%): Ecuaciones lineales, factorización, sistemas de ecuaciones. Practica despejar variables.
Geometría (20%): Áreas, perímetros, volúmenes, ángulos, triángulos. Memoriza las fórmulas más importantes.
Estadística (15%): Media, mediana, moda, probabilidad básica. Practica con conjuntos de datos reales.
Error 1 — Saltarse pasos: Los errores de matemáticas suelen ocurrir cuando se saltan pasos para ir más rápido. Escribe cada paso, aunque te parezca obvio.
Error 2 — No verificar: Siempre sustituye tu respuesta en la ecuación original para verificar que es correcta. Toma solo 30 segundos y puede salvarte de perder puntos.
Error 3 — Confundir fórmulas similares: El área del triángulo (base×altura÷2) se confunde con el perímetro (suma de los tres lados). Entiende qué mide cada fórmula.
Error 4 — Operaciones con fracciones: Para sumar fracciones necesitas denominador común. Para multiplicar, no. Para dividir, invierte la segunda fracción y multiplica.
Semana 1: Repasa aritmética básica — fracciones, decimales, porcentajes, potencias y raíces.
Semana 2: Álgebra — ecuaciones lineales, factorización, sistemas de ecuaciones.
Semana 3: Geometría — áreas, perímetros, volúmenes, triángulos, ángulos.
Semana 4: Simulacros completos en tiempo real y repaso de temas débiles.
🧮 Herramientas de práctica gratuitas
Khan Academy: khanacademy.org — videos y ejercicios gratuitos de todos los temas. Desmos: desmos.com — graficadora gratuita para visualizar funciones. Wolfram Alpha: wolframalpha.com — resuelve y explica cualquier problema matemático.