Unit 14: Measures of Center and Data Displays
Boiling a whole data set down to one typical number, and the displays that show its shape, spread, and outliers.
5 topics · 18 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Sampling and Why It Matters
- How it worksHow does a random sample avoid favoring any one group over another in a population?
- Common mistakeWhy doesn't surveying every student who happens to walk by the school's front doors count as a random sample?
- Going furtherWhat happens to how trustworthy a sample's results are as the sample size gets bigger?
Your turn1 of 2
A researcher wants opinions from all 757 students in a school. They survey the first 36 students who happen to walk by the front doors that morning. Is this a convenience sample rather than a random one?Mean, Median, and Mode
- How it worksHow do you calculate the mean, find the median, and identify the mode of the same data set?
- Worked exampleFind the mean, median, and mode of the data set 4, 7, 7, 9, 12, 40.
- Going furtherWhat happens to the mean versus the median when one extreme outlier is added to a data set?
- Common mistakeWhy isn't the mean always the same as the middle value in a data set?
Your turn1 of 2
Five friends scored 35, 33, 47, 15, and 4 points in a game. What is the mean score?Range and Mean Absolute Deviation
- How it worksHow does mean absolute deviation measure the typical distance each data point sits from the mean?
- Worked exampleFind the range and the mean absolute deviation of the data set 2, 4, 4, 6, 9.
- Common mistakeWhy doesn't the range alone tell you how spread out most of the data actually is?
Your turn1 of 2
The shortest kid in a class is 14 inches tall, and the tallest is 46 inches tall. What is the range of heights?Box Plots
- How it worksHow do the five-number summary's minimum, quartiles, and maximum build the box and whiskers of a box plot?
- Worked exampleBuild a box plot for the data set 3, 7, 8, 10, 12, 14, 19.
- Common mistakeWhy doesn't the line inside a box plot always sit in the exact middle of the box?
Your turn1 of 2
A box plot of test scores has a first quartile of 15 and a third quartile of 40. What is the interquartile range?Histograms
- How it worksHow does a histogram's bar height show how many data points fall into each equal-width interval?
- Worked exampleBuild a histogram for 20 quiz scores grouped into the intervals 0 to 59, 60 to 69, 70 to 79, 80 to 89, and 90 to 100.
- Worked exampleCompare the shapes of the same histogram built with intervals of width 5 instead of width 10.
- Common mistakeWhy isn't a histogram just a bar graph with the bars pushed together for no reason?
- Ties togetherHow does changing a histogram's interval width connect to the same grouping idea behind a box plot's quartiles?
Your turn1 of 2
A histogram of quiz scores has one bar with a frequency of 21 students and another with a frequency of 20 students. How many students are in just those two bars?