Describe Data by Range and Interquartile Range Challenge

Grade 6 Math · Unit 2 Challenge Studio (6.DS.3) · Lesson 2-5
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I can find the range and the interquartile range of a data set and use them to describe how spread out the data is.Puedo hallar el rango y el rango intercuartílico de un conjunto de datos y usarlos para describir qué tan dispersos están los datos.

MissionMisión · Rooftop GardenJardín en la azotea · night shiftturno de noche

Grow your skills.Haz crecer tus habilidades.

Dusk settles over the garden and the grow-lights flicker on. One strange plant is far taller than the rest, and only a careful gardener can tell which measure of spread can be trusted.

Atardece en el jardín y se encienden las luces de cultivo. Una planta extraña es mucho más alta que las demás, y solo un jardinero atento puede decir en qué medida de dispersión se puede confiar.

Word bankBanco de palabras 5 words5 palabrasrange, interquartile range (IQR), quartile, …rango, rango intercuartílico (RIC), cuartil, …
rangerango
The distance from the least value to the greatest value: greatest − least.La distancia del valor menor al valor mayor: mayor − menor.
interquartile range (IQR)rango intercuartílico (RIC)
The spread of the middle half of the data: Q3 − Q1.La dispersión de la mitad central de los datos: Q3 − Q1.
quartilecuartil
One of the values that cut ordered data into four equal parts.Uno de los valores que dividen los datos ordenados en cuatro partes iguales.
variabilityvariabilidad
How much the values in a data set differ from one another.Cuánto difieren entre sí los valores de un conjunto de datos.
extreme valuevalor extremo
The least or greatest value, far from the rest.El valor menor o mayor, lejos del resto.

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.

  1. 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.

  1. Find the error
  2. Two students both scored 80 on a make-up test — one joins Class A (range 28, IQR 13) and one joins Class B (range 20, IQR 8). Both classes have a median of 81. Predict how each class's IQR changes, and explain your reasoning.
  3. The rooftop garden measured 11 sunflowers. Heights in centimeters: 48, 62, 55, 71, 39, 66, 58, 44, 80, 52, 60. Fill in each measure. Q1 and Q3 are the medians of the lower and upper halves. If the count is odd, leave the median out of both halves.
  4. The box plots show the weights, in grams, of tomatoes from two garden beds. Both beds have a median of 60 grams. Which statement is true?
    • Bed A has both the larger range and the larger IQR
    • Bed B has both the larger range and the larger IQR
    • B's range is 80 g; A's middle half spreads 16 g.
    • The two beds are equally spread out because their medians match
  5. A garden crew measured 8 bean pods (cm): 12, 14, 15, 15, 17, 18, 19, 21. Then they found a 9th pod, 45 cm long. Fill in the range and the IQR before and after the new pod. Q1 and Q3 are the medians of the lower and upper halves. If the count is odd, leave the median out of both halves.
  6. A garden bed’s data have a minimum of 6, Q1 = 18, an IQR of 14 and a range of 40. What is the maximum value?

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.

  1. Sort each description: does it fit the range, the IQR, or both?
  2. Build two sets of 8 results that have the same range but different interquartile ranges. Say which set is more consistent in its middle half and explain how you know.
  3. 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.

  1. Ayesha has a data set with minimum 22, Q1 31, median 40, Q3 47 and maximum 60. She finds the range and the IQR.
  2. Bao finds the range of the seed counts 14, 9, 22, 6, 18, written in the order the pods were opened.
  3. Greta compares two herb beds. Bed 1: 10, 15, 20, 25, 30. Bed 2: 18, 19, 20, 21, 22.
  4. Snail lengths in millimeters are 12, 13, 13, 14, 15, 15, 16, 48. Hugo says the range, 36, shows how spread out most snails are. Noa says the IQR (Q3 − Q1), 2.5, is better because the 48 is far from the rest. Who is right?
    • Hugo, because the range uses every value
    • Hugo, because the range is always the smaller measure
    • Both are equally good because both use subtraction
    • Noa, because the IQR ignores the extreme 48
  5. What is the best next move?
    • Compare the ranges, because they cover every score in each class.
    • Compare the medians, because they show how close the scores are.
    • Compare the IQRs, because they cover the middle half of each class.
  6. 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.

  1. Seven pepper plants made 27, 14, 33, 9, 21, 38, 16 peppers. What is the range?
  2. Ten tomato plants have these numbers of ripe tomatoes, in order: 5, 8, 9, 11, 12, 14, 15, 19, 22, 30. Q1 and Q3 are the medians of the lower and upper halves. What is the IQR?
  3. The box plots show the heights of plants from two seed packets. Which packet gives more even plants, with a smaller IQR?
    • Packet Y: its IQR is 6, compared with 20
    • Packet X: its range is 40
    • Neither, because both medians are 30
    • Packet X: its IQR is 20, the larger number
  4. Can the IQR of a data set be larger than its range?
    • Yes, if the data have an extreme value
    • No; the IQR is part of the range.
    • Yes, because Q3 + Q1 is bigger than the maximum
    • Yes, when the median is large
  5. A set of data has a range of 28 and a maximum of 45. What is the minimum?
  6. Create your own problem. Write two data sets of 7 or 8 numbers about two garden beds that have the same median but different spread. Find the range and the IQR of each, and explain which bed is more consistent. Use the words range, quartile, interquartile range and vary.