Family Math Studio Grade 6 Math · Neft Teacher

Family Math Studio · Lesson guide Guía de la lección

Unit 2, Lesson 5: Describe Data by Range and Interquartile Range

Standard 6.DS.3

What students are learning Qué aprenden

Key idea: The range tells how spread out all of the data is: range = greatest number − least number. The interquartile range (IQR) tells how spread out the middle half of the data is: IQR = Q3 − Q1.Idea clave: El rango dice qué tan separados están todos los datos: rango = número mayor − número menor. El rango intercuartílico dice qué tan separada está la mitad central de los datos: rango intercuartílico = Q3 − Q1.

Words to know Palabras clave

Range and Interquartile Range Rango y rango intercuartílico
Two numbers that tell how far apart the data is.
Dos números que dicen qué tan separados están los datos.
Range Rango
How far it is from the least to the greatest.
Qué tan lejos está del valor menor al mayor.
Quartile Cuartil
One of three numbers that split data into four equal parts.
Uno de tres números que dividen los datos en cuatro partes iguales.
Interquartile range Rango intercuartílico
The distance across the middle half of the data.
La distancia que cubre la mitad central de los datos.
Variability Variabilidad
How far apart the numbers are.
Qué tan separados están los números.
Measure of variation Medida de variación
One number that tells how far apart the data is.
Un número que dice qué tan separados están los datos.
Extreme value Valor extremo
The lowest or highest value, far from the rest.
El valor más bajo o más alto, lejos de los demás.

Sentence starters Frases para empezar

I know ___ because ___.

First, I ___. Then, I ___.

The answer is ___, so ___.

How we did it in class today Cómo lo hicimos hoy en clase

  1. Here are 20 history test scores in order: 68, 70, 73, 74, 75, 76, 77, 80, 82, 83, 84, 85, 86, 86, 88, 88, 90, 90, 93, 94. Ordering them first is what makes every step after this possible.
  2. Range: I subtract the least value from the greatest. 94 − 68 = 26. The scores span 26 points from end to end.
  3. Now the quartiles. The median splits the 20 scores into two halves of 10. The median is halfway between the 10th and 11th values: (83 + 84) ÷ 2 = 83.5.
  4. Q1 is the median of the lower 10 values: halfway between 75 and 76, so Q1 = 75.5. Q3 is the median of the upper 10: halfway between 88 and 88, so Q3 = 88.
  5. Interquartile range: IQR = Q3 − Q1 = 88 − 75.5 = 12.5. The middle half of the students' scores differed by only 12.5 points, even though the full range was 26.

Play with today's math Jueguen con las matemáticas

Interactive Lesson Model — This is the exact same interactive tool your student used in class today. Change the numbers and watch what happens!

Modelo interactivo de la lección — Esta es la misma herramienta interactiva que su estudiante usó en clase hoy. ¡Cambie los números y observe qué sucede!

Works on a phone, a tablet, or a computer. Nothing to install, nothing to sign in to.

Try this together Inténtenlo juntos

Pick one question to talk about. You don't need to do them all!

A box plot shows how many minutes students read each night. Q1 = 14 and Q3 = 32. The least value is 6 and the greatest value is 45. What is the IQR, and what does it tell you?

  1. IQR = 23; 23 is halfway between the quartiles
  2. IQR = 39; the data spans 39 minutes from end to end
  3. IQR = 18; the middle half of the data spans 18 minutes
  4. IQR = 46; the quartiles add to 46
Check the answer

The answer is: IQR = 18; the middle half of the data spans 18 minutes

Take-home sheet Hoja para llevar a casa

Lesson 2.5: Print the sheet (PDF) · Answers and talk notes (PDF) · Edit it (Word)

Lección 2.5: Imprimir la hoja (PDF) · Respuestas y notas para conversar (PDF) · Editarla (Word)

If they get stuck... Si se traban...

Watch out for this: A common mistake with Range and Interquartile Range is adding the two quartiles instead of subtracting them — writing IQR = Q3 + Q1. With Q1 = 42 and Q3 = 58 that gives 100, which is larger than the data set's entire range of 20. Every measure of variation is a DIFFERENCE, and the IQR can never exceed the range, because the middle half is part of the whole span. If your IQR comes out bigger than your range, you added when you should have subtracted.

Try asking: "Can you show me how you got that? Did we miss a step?"
Pregunte: «¿Puedes mostrarme cómo lo hiciste? ¿Nos saltamos algún paso?» Hablar de las matemáticas en voz alta ayuda mucho.

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