I can choose the best measure of center for a data set based on its shape.Puedo elegir la mejor medida de tendencia central para un conjunto de datos según su forma.
MissionMisión · Home FieldCancha local · night shiftturno de noche
Train like a champion.Entrena como un campeón.
It is championship night at Home Field. The broadcast crew will read your numbers on live TV, and a misleading average could fool thousands of fans. Choose the measures that keep the broadcast honest.
Es la noche del campeonato en Home Field. El equipo de transmisión leerá tus números en vivo, y un promedio engañoso podría confundir a miles de aficionados. Elige las medidas que mantengan honesta la transmisión.
Word bankBanco de palabras 5 words5 palabrasoutlier, skewed, median, …valor atípico, sesgado, mediana, …
- outliervalor atípico
- A value that is much bigger or smaller than the rest of the data.Un valor mucho mayor o menor que el resto de los datos.
- skewedsesgado
- Data bunched on one side with a long tail on the other side.Datos agrupados de un lado con una cola larga del otro lado.
- medianmediana
- The middle value when the data is in order. An outlier barely moves it.El valor del medio cuando los datos están en orden. Un valor atípico casi no la mueve.
- meanmedia
- Add all the values and divide by how many there are. An outlier pulls it.Suma todos los valores y divide entre cuántos hay. Un valor atípico la jala.
- variabilityvariabilidad
- How spread out the data values are.Qué tan dispersos están los valores de los datos.
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 Reasoning Error
- A local newspaper reports that the average home price in a neighborhood is $450,000. The actual prices are: $180K, $200K, $190K, $210K, $195K, $1,725K. Is the reporter's claim misleading? Calculate the mean and median and explain which better represents a 'typical' home price.
- Sort each real-world situation into whether the mean or median is more commonly reported.
- The Home Field cycling club logged the length of its last 9 rides, shown in the dot plot. The newsletter wants one number for a typical ride. Which statement is correct?
- The mean is 26 km and the median is 21 km. Use the mean, because it counts every ride.
- The mean is 26 km and the median is 21 km. Use the median, because the 70 km ride pulls the mean up.
- Without the 70 km ride, the mean is 20.5 km and the median is 21 km. Either works, so leave the long ride out.
- The mean is 26 km and the median is 21 km. Use the range, 52 km, because it shows the biggest ride.
- A center's rebounds in 8 games are shown in the dot plot. Which pair of measures should the stats sheet report, and what are their values?
- Mean 8.5 and MAD 4.625
- Median 6 and MAD 4.625
- Mean 8.5 and IQR 2.5
- Median 6 and IQR 2.5
- A swim team's practice minutes for two weeks are listed in the first column. In Week 2 the team added one marathon session. Fill in each mean, each median, and the gap between them (mean − median).
- The dot plot shows the water bottles the team used in each of its last 8 games. The manager must order for the next 10 games. Another hot day, like the 49-bottle game, can happen. Which order makes the most sense?
- 250 bottles: 25 per game × 10 covers a hot game.
- 220 bottles: the median is 22, the typical game, times 10 games.
- 490 bottles: order for the biggest game, 49, every time.
- 200 bottles: that was the total for the last 8 games.
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.
- Home Field has six data sets. Sort each one by the pair of measures that describes it best.
- Make up eight game scores with one outlier. Write two short reports about the same data, one using the mean and one using the median. Recommend which report a coach should trust and explain why.
- 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.
- A student reported a goalkeeper's saves. One step in the report goes wrong. Tap the first step that is wrong.
- A tennis coach tried to find the median serve speed. One step goes wrong. Tap the first step that is wrong.
- A runner's coach wrote this report. One step goes wrong. Tap the first step that is wrong.
- After a sprint drill, Ana and Ben each reported the spread of the recovery times in the dot plot. Ana said "median 15, range 34." Ben said "median 15, IQR 3.5." Who chose the better spread measure?
- Ana, because the range uses the smallest and largest times, so it shows all the data.
- Both are fine, because both reported the same median.
- Ben, because the 46 stretches the range, but the IQR describes the middle half of the times.
- Neither, because skewed data needs the mean and MAD for spread.
- What is the best next move?
- Compare the means, because they use every run.
- Choose Team B because it has the fastest single run, 30 s.
- Compare the ranges to see which team is faster.
- Compare the medians, since one run of 70 s pulls B's mean up.
- 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.
- Nine athletes took the Home Field fitness test. The dot plot shows how many push-ups each one completed. The mean is 16 push-ups. Which statement is correct?
- The median is 16, the same as the mean, so either measure works.
- The median is 19, but the mean is better because it uses all nine scores.
- Median 19: the two low scores pull the mean down.
- The median is 18, the 4th score, because 9 ÷ 2 = 4.5 rounds down.
- The league reports attendance with the median and IQR. Attendance at 9 home games, in hundreds of fans, is shown in the dot plot. What is the IQR?
- Two relay teams' 100 m times (seconds) are shown in the box plots. Which statement is best supported by the median and the IQR?
- The Rams are faster, because their quickest time is 10.9 s.
- Same median (12.2 s); Hawks have a smaller IQR (0.8 s vs. 1.6 s).
- The Rams are more consistent, because their box is wider.
- The teams are equally consistent, because they have the same median.
- Home Field's account gained 10, 12, 13, 15, and 40 hundred followers after five games. A viral video then changes the last number to 400. Which statement is true?
- Only the mean changes, from 18 to 90; the median stays 13.
- Only the median changes, because it is the middle value.
- Both change by the same amount.
- Neither changes, because 40 and 400 are both the biggest number.
- A swimmer's 100 m practice times are shown in the dot plot. The 75 s lap happened when her goggles slipped. The coach reports the median. Which explanation is complete and correct?
- The median is better because it is the middle number.
- The 75 s lap pulls the mean to 61.7 s; the median better shows a typical lap.
- The 75 s outlier pulls the median up, so the median is not typical.
- The data is skewed, so the mean cannot be found.
- Make up a data set of 6 to 8 numbers from a sport you like, so that the median is a better center than the mean. Write the numbers, find the mean and the median, and explain which one you would report and why.