Represent and Describe Data in a Histogram Challenge

Grade 6 Math · Unit 2 Challenge Studio (6.DS.5) · Lesson 2-2
Progress: 0 / 30

I can make and read a histogram to display data in intervals.Puedo hacer y leer un histograma para mostrar datos en intervalos.

MissionMisión · Pixel ArcadeArcade de píxeles · night shiftturno de noche

Clear every level.Supera todos los niveles.

After closing time the cabinets hum in the dark. A glitch has scrambled the leaderboard, and only a careful bar-builder can rebuild each histogram and spot the pattern.

Después de cerrar, las máquinas zumban en la oscuridad. Una falla revolvió el marcador, y solo un constructor de barras cuidadoso puede reconstruir cada histograma y descubrir el patrón.

Word bankBanco de palabras 5 words5 palabrashistogram, frequency, interval, …histograma, frecuencia, intervalo, …
histogramhistograma
A graph that groups numbers into equal intervals. Its bars touch, and each bar’s height is a count.Una gráfica que agrupa números en intervalos iguales. Sus barras se tocan y la altura de cada barra es un conteo.
frequencyfrecuencia
How many data values fall in an interval. It is the height of the bar.Cuántos datos caen en un intervalo. Es la altura de la barra.
intervalintervalo
An equal-sized range of numbers used to group data, such as 10–19.Un rango de números del mismo tamaño que se usa para agrupar datos, como 10–19.
frequency tabletabla de frecuencias
A table that lists each interval and how many values fall in it.Una tabla que muestra cada intervalo y cuántos valores caen en él.
distributiondistribución
How the data are spread out, including where the peak is and which way the tail points.Cómo están repartidos los datos, incluyendo dónde está el pico y hacia dónde apunta la cola.

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 Histogram Error
  2. A teacher collected test scores and made two different histograms — one with intervals of 5 (50–54, 55–59, etc.) and one with intervals of 20 (50–69, 70–89, 90–109). Both use the same data. How might the two histograms look different? Which interval size gives you more detail about the distribution? When might the larger interval be better?
  3. A histogram of points-per-game has its tallest bars on the LEFT (low scores) and a long tail stretching RIGHT toward a few high scorers. How is this distribution described?
    • Skewed left
    • Symmetric
    • Bimodal (two equal peaks)
    • Skewed right
  4. Pixel Arcade tracked the tickets won by 24 players: 33, 10, 57, 21, 4, 45, 29, 38, 19, 50, 26, 42, 13, 68, 31, 9, 49, 20, 35, 52, 17, 40, 24, 30. Count how many values fall in each interval of 10, then add the frequencies to check your work.
  5. The histogram shows the scores of 36 players on Space Blasters. A player earns a bonus game with a score of 60 or more. How many players earn a bonus game?
  6. The arcade owner says, “More than half of our players spent less than 15 minutes on Racing Rally.” The histogram shows 35 players. Is she right?
    • No. The tallest bar has only 11 players, which is less than half of 35.
    • No. Only 4 + 11 = 15 players spent less than 10 minutes.
    • Yes. The first three bars hold 24 of 35 players, over half.
    • Yes. The histogram has 6 bars and 3 of them are below 15.
  7. High scores at the arcade run from 12 to 87. Which set of intervals could make a correct histogram of every score?
    • 10–19, 20–29, 30–39, 40–49, 50–59, 60–69, 70–79, 80–89
    • 10–20, 20–30, 30–40, 40–50, 50–60, 60–70, 70–80, 80–90
    • 10–19, 20–29, 30–39, 40–49, 60–69, 70–79, 80–89
    • 10–19, 20–29, 30–49, 50–69, 70–89

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. A histogram has the intervals 0–19, 20–39 and 40–59. Sort each score into the interval where its tally goes.
  2. Invent 10 game scores and group them into equal intervals. Write a headline that your histogram supports. Then write one claim a histogram cannot support, and explain why it cannot.
  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. Noor counted the levels cleared by 7 players: 7, 10, 14, 20, 23, 29, 30. She is making a frequency table with the intervals 0–9, 10–19, 20–29 and 30–39.
  2. Dmitri wants a histogram of the minutes 8 players spent on Pinball: 14, 22, 31, 38, 44, 53, 58, 61. He chooses intervals and counts.
  3. Kai reads a histogram of the best scores on Sky Runner. He says the tallest bar tells him who played best.
  4. This histogram shows the coins collected in each run of Maze Quest. Amara says it is skewed right because the tail stretches to the right. Luca says it is skewed left because most of the data is on the left. Who is right?
    • Luca, because a skew is named for the side with most of the data
    • Both are right, because a skew can be named either way
    • Neither, because the histogram is symmetric
    • Amara, because a skew is named for the side where the long tail points
  5. What is the best next move?
    • Count each 20 a second time in 10–19, because 20 touches that interval.
    • Draw the bars with heights 0, 10, 20 and 30, the start of each interval.
    • Draw the bars with gaps so the intervals do not touch.
    • Add the counts and check the total against the number of scores.

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. The histogram shows the coins collected in each run of Treasure Tunnel. How many runs are shown?
  2. Four scores are 29, 30, 39 and 40. A histogram uses the intervals 20–29, 30–39 and 40–49. Which statement is correct?
    • 29 and 30 go in the same bar
    • 30 and 39 share a bar.
    • 39 and 40 go in the same bar
    • All four scores go in the same bar
  3. The histogram shows the scores of 37 players on Dance Beat. Which phrase best describes its shape?
    • Skewed right: the tallest bars are on the right
    • Symmetric: the bars are the same on both sides
    • Flat: all the bars are about the same height
    • Skewed left: the tail points left
  4. Which data should be shown in a histogram instead of a bar graph of categories?
    • The favorite cabinet chosen by each player
    • The color of the prize each player picked
    • Minutes spent at the claw machine
    • The name of the game each player started with
  5. Pixel Arcade’s histogram shows 30 players in five bars. Four of the bars have heights 5, 9, 6 and 2. What is the height of the fifth bar?
  6. Create your own problem. Make up 12 scores for a game at Pixel Arcade. Choose equal intervals, write a frequency table, and describe the shape of your histogram. Use the words histogram, frequency, interval and distribution.