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Unit 17: Statistics and Data

A single number can summarize a whole data set's center or spread, and a scatter plot turns two related variables into one visible trend.

6 topics · 19 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.

Measures of Center

  1. How it worksHow do the mean, median, and mode each summarize a data set's center in a different way?
  2. Worked exampleFind the mean and median of the data set 4, 7, 7, 9, 40.
  3. Common mistakeWhy isn't the median always closer to the middle of a data set than the mean is, regardless of skew?
Your turn1 of 2
Find the mean of the data set 4, 8, 13, 15, 36.

Measures of Spread

  1. How it worksHow does the range and the interquartile range each measure how spread out a data set is?
  2. Worked exampleFind the range and interquartile range of the data set 2, 5, 6, 9, 12, 15, 20.
  3. Going furtherWhat happens to a data set's spread when you add one extreme outlier to it?
  4. Worked exampleFind the standard deviation of the data set 2, 4, 4, 6.
Your turn1 of 2
Find the range of the data set 2, 5, 9, 11, 13, 16, 23.

Box Plots

  1. How it worksHow do the five-number summary values turn into the box and whiskers of a box plot?
  2. Worked exampleBuild the box plot for the data set 3, 7, 8, 10, 12, 14, 19.
  3. Common mistakeWhy doesn't a longer whisker on a box plot mean that side has more data points in it?
Your turn1 of 2
Find the median for the data set 2, 5, 9, 11, 13, 16, 23.

Scatter Plots and Correlation

  1. How it worksHow does the tightness and direction of a scatter plot's pattern reveal the strength of a correlation?
  2. Worked exampleShow me what a scatter plot of hours studied versus test score looks like for a strong positive correlation.
  3. Common mistakeWhy doesn't a strong correlation between two variables prove that one causes the other?
Your turn1 of 2
A scatter plot of hours studied versus test score shows a strong positive linear pattern following score = 6 times hours + 53. Predict the score for 8 hours studied.

The Line of Best Fit

  1. How it worksHow does a line of best fit get positioned to minimize its overall distance from every data point?
  2. Worked exampleFind the equation of the line of best fit for data points roughly following (1, 3), (2, 5), (3, 8), (4, 10).
  3. Going furtherWhat happens to a line of best fit's slope when a new data point far above the trend gets added?
Your turn1 of 2
Data points closely follow a line through (2, 6) and (9, 19). Write the line of best fit, y, as a function of x.

Two-Way Frequency Tables

  1. How it worksHow do row totals and column totals in a two-way table let you compute relative frequencies?
  2. Worked exampleFind the relative frequency of soccer preference among freshmen in a two-way table showing 30 freshmen, 12 of whom prefer soccer.
  3. Ties togetherHow does a two-way frequency table's relative frequencies connect to the idea of correlation in a scatter plot?
Your turn1 of 2
A two-way table shows 42 freshmen, 15 of whom prefer soccer. Find the relative frequency of soccer preference among freshmen, as a decimal.