I can find the mean absolute deviation (MAD) to describe how spread out data is.Puedo hallar la desviación media absoluta (DAM) para describir qué tan dispersos están los datos.
MissionMisión · Sound StudioEstudio de sonido · night shiftturno de noche
Mix the track, then check the math.Mezcla la pista y revisa las matemáticas.
The studio lights dim to a single glow. One track keeps drifting off the beat, and only a sharp ear can use the MAD to tell a steady mix from a wild one.
Las luces del estudio bajan a un solo resplandor. Una pista se sale del ritmo, y solo un oído agudo puede usar la DAM para distinguir una mezcla estable de una desordenada.
Word bankBanco de palabras 5 words5 palabrasmean absolute deviation (MAD), deviation, absolute value, …desviación media absoluta (DAM), desviación, valor absoluto, …
- mean absolute deviation (MAD)desviación media absoluta (DAM)
- The average distance of the data values from the mean. It describes spread.La distancia promedio de los valores a la media. Describe la dispersión.
- deviationdesviación
- How far a value is from the mean: value − mean. It can be negative.Qué tan lejos está un valor de la media: valor − media. Puede ser negativa.
- absolute valuevalor absoluto
- The distance of a number from zero. It is never negative.La distancia de un número a cero. Nunca es negativo.
- spreaddispersión
- How far apart the data values are.Qué tan separados están los valores de los datos.
- meanmedia
- The sum of the values divided by how many values there are.La suma de los valores dividida entre cuántos valores hay.
Stage 1 of 5Etapa 1 de 5
Start StrongEmpieza fuerte
Each rung is harder than the last, and the numbers change every time.
Cada peldaño es más difícil que el anterior y los números cambian cada vez.
- 6 fresh problems with new numbers each time (interactive only).
Stage 2 of 5Etapa 2 de 5
Stretch Your ThinkingAmplía tu pensamiento
Plan, solve, then check that your answer makes sense.
Planea, resuelve y revisa que tu respuesta tenga sentido.
- Find the MAD Error
- Two basketball teams both average 75 points per game. Team A's last 5 scores: 73, 76, 74, 77, 75. Team B's last 5 scores: 60, 90, 65, 85, 75. Calculate the MAD for each team and explain which team a coach would prefer if they need predictable scoring.
- Five tracks in the Sound Studio last 12, 15, 9, 18, 11 minutes. Find the mean, the distance of each track from the mean, and the MAD.
- Two studio groups practiced for 4 days. Group A played 9, 9, 11 and 11 minutes. Group B played 4, 8, 12 and 16 minutes. Both groups have a mean of 10 minutes. Which statement is true?
- Group B is more spread out: its MAD is 4 minutes and Group A’s is 1
- The groups are equally spread out because their means are equal
- Group A is more spread out: its MAD is 1 and Group B’s is 4
- Group B is more spread out because 16 is greater than 11
- A MAD uses 4 values. Three of the values are 1, 5 and 2 minutes from the mean. The MAD is 3 minutes. How far from the mean is the fourth value?
- Each dot is one drum track’s length in minutes. The mean is 6. Which is the best estimate of the MAD?
- 6
- 1
- 4
- 0
Stage 3 of 5Etapa 3 de 5
InvestigateInvestiga
Use the model to test an idea. Then check it.
Usa el modelo para probar una idea. Luego compruébala.
- Find the MAD of each data set in your head. Then sort the sets by the size of the MAD.
- Build two sets of four numbers that both have a mean of 10 but different MADs. Show the distances from the mean for each set. Say which set is more spread out and how you know.
- 4 fresh problems with new numbers each time (interactive only).
Stage 4 of 5Etapa 4 de 5
Find and FixEncuentra y corrige
Somebody made a mistake. Find the step and fix it.
Alguien cometió un error. Encuentra el paso y corrígelo.
- Imani finds the MAD of the beat counts 4, 10, 7, 11 and 8. The mean is 8.
- Jun finds the MAD of the volume settings 1, 2, 3 and 10. The median is 2.5 and the mean is 4.
- Cleo finds the MAD of the amp levels 4, 8, 12 and 8. The mean is 8.
- A data set has a MAD of 0. Sam says all the values are equal. Rae says the mean must be 0. Who is right?
- Rae, because MAD and mean are the same number
- Both, because a mean of 0 makes all values equal
- Sam, because every distance from the mean must be 0
- Neither, because a MAD is never 0
- What is the best next move?
- Say the MAD is 20, since that is the total of the distances.
- Divide 20 by 15, the mean.
- Divide 20 by 5, the number of values.
- Subtract the smallest distance from the greatest: 8 − 1.
- 1 fresh problem with new numbers each time (interactive only).
Stage 5 of 5Etapa 5 de 5
Prove Your UnderstandingDemuestra tu comprensión
Say how sure you are, solve, then create a problem of your own.
Di qué tan seguro estás, resuelve y luego crea un problema tuyo.
- Six speakers play 14, 18, 20, 12, 16, 22 watts. What is the MAD?
- Studio X has song lengths with a MAD of 2.5 minutes. Studio Y has song lengths with a MAD of 6 minutes. Which statement is correct?
- Studio Y’s song lengths are more spread out
- Studio X’s song lengths are more spread out
- Studio Y’s songs are longer
- The two studios have the same spread
- A drummer plays 40, 50, 60, 50 beats per measure. What is the MAD?
- The MAD of a band’s practice times is 4 minutes. What does that tell you?
- Every practice time is exactly 4 minutes from the mean
- Times average about 4 minutes from the mean.
- The mean practice time is 4 minutes
- The longest time is 4 minutes more than the shortest
- A volume level is 7 units away from a mean of 12. Which values could it be?
- Only 19
- −7 or 7
- Only 5
- 5 or 19
- Create your own problem. Write a data set of 4 or 5 numbers about a Sound Studio, such as song lengths. Find the mean and the MAD, showing each distance. Explain what the MAD tells you about the spread. Use the words mean absolute deviation, deviation, absolute value and spread.