Represent and Describe Data in a Box Plot Challenge

Grade 6 Math · Unit 2 Challenge Studio (6.DS.5) · Lesson 2-4
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I can make and read a box plot to summarize a data set.Puedo hacer y leer un diagrama de caja para resumir un conjunto de datos.

MissionMisión · Corner KitchenCocina de la esquina · night shiftturno de noche

Cook up the right answer.Cocina la respuesta correcta.

After the dinner rush the kitchen lights dim. Two stations send back their ticket times, and only a careful cook can build and compare their box plots.

Después de la hora pico de la cena, las luces de la cocina bajan. Dos estaciones devuelven sus tiempos de pedidos, y solo un cocinero cuidadoso puede construir y comparar sus diagramas de caja.

Word bankBanco de palabras 5 words5 palabrasbox plot, quartile, interquartile range, …diagrama de caja, cuartil, rango intercuartílico, …
box plotdiagrama de caja
A graph that shows the five-number summary with a box and two whiskers.Una gráfica que muestra el resumen de cinco números con una caja y dos bigotes.
quartilecuartil
A value that helps split the data into four equal parts. Q1 and Q3 are quartiles.Un valor que ayuda a dividir los datos en cuatro partes iguales. Q1 y Q3 son cuartiles.
interquartile rangerango intercuartílico
The length of the box: Q3 − Q1. It shows the spread of the middle half.La longitud de la caja: Q3 − Q1. Muestra la dispersión de la mitad central.
five-number summaryresumen de cinco números
The minimum, Q1, median, Q3 and maximum of a data set.El mínimo, Q1, la mediana, Q3 y el máximo de un conjunto de datos.
whiskerbigote
The line from the box out to the least or greatest value.La línea que va de la caja hasta el valor menor o mayor.

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 Box Plot Error
  2. Two basketball teams played 9 games each. Team A: 40, 42, 44, 46, 48, 50, 52, 54, 56. Team B: 30, 35, 40, 45, 48, 50, 55, 60, 65. Find the five-number summary and IQR for each team. Which team is more consistent? Which has a wider spread in the middle 50%?
  3. Match each box plot feature with what it tells you about the data.
  4. Corner Kitchen timed 9 cakes in the oven. Minutes: 38, 25, 31, 44, 29, 35, 41, 27, 33. Order the times. Fill in the five-number summary and the IQR. Q1 and Q3 are the medians of the lower and upper halves. If the count is odd, leave the median out of both halves.
  5. The box plot shows the prep times of 40 dishes. About how many dishes took longer than 36 minutes?
  6. The box plots show the ticket times, in minutes, for two stations. Both stations have the same median. Which statement is correct?
    • The Grill is slower because its box sits higher
    • Salad's IQR is 18 min; Grill's is 8, so Salad has more spread.
    • The two stations have equal spread because their medians match
    • The Grill has the larger IQR: 8 minutes
  7. The box plot shows a five-number summary for 8 order times.
    • 3, 5, 6, 8, 8, 12, 14, 15
    • 3, 4, 6, 8, 8, 10, 13, 15
    • 3, 4, 6, 7, 9, 11, 13, 15
    • 3, 4, 5, 7, 9, 12, 12, 15

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 by the part of a box plot it describes.
  2. Create eight order times with a median of 20 and an interquartile range of 10. Write your five-number summary and explain how you found each quartile as the median of a half.
  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. Yusuf finds Q1 and Q3 for the 7 cooking times 2, 5, 6, 8, 9, 11, 14, which are already in order. Use the rule that the median is left out of both halves when the count is odd.
  2. Mina’s box plot has minimum 6, Q1 14, median 20, Q3 27 and maximum 41. She finds the IQR.
  3. Dev reads a box plot of delivery times. His claim: the long right whisker shows that most of the data are on the right.
  4. These box plots show lunch-rush times for two kitchens. Selam says Kitchen B has the longer box, so it has more spread. Lucía says Kitchen B has times that are all higher but the same spread. Who is right?
    • Lucía: both boxes have equal spread, but B is higher.
    • Selam, because Kitchen B’s box is farther to the right
    • Neither, because the whiskers are different
    • Both, because Kitchen B is higher and longer
  5. What is the best next move?
    • Use 21, the middle of the upper half, as Q3.
    • Take 15 out of the upper half before finding Q3.
    • Use 30 − 4 as the IQR.
    • Draw the box from the median, 15, to the maximum, 30.

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. Ten soups were timed in minutes: 14, 9, 22, 17, 12, 30, 19, 11, 25, 16. Q1 and Q3 are the medians of the lower and upper halves. What is the IQR?
  2. The box plot shows the weights of 80 bread loaves. About what fraction of the loaves weigh between the median and the maximum?
    • One quarter
    • One half
    • Three quarters
    • All of them
  3. A box plot of oven temperatures has an IQR of 14 degrees and Q3 = 34. What is Q1?
  4. Which five numbers are needed to draw a box plot?
    • Mean, median, mode, range, IQR
    • Minimum, mean, median, mode, maximum
    • Q1, Q2, Q3, IQR, range
    • Minimum, Q1, median, Q3, maximum
  5. The box plot shows the cooking times of a menu. What is the range of the times?
  6. Create your own problem. Write 9 or 10 cooking times for a kitchen, find the five-number summary and the IQR, and describe what your plot would look like. Use the words box plot, median, quartile and interquartile range.