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* teach about how to make a box plot, introduce comparing box plots and histograms, incorporate variability into all lesson references to statistical questions, add a page for practicing making a box plot by hand (see #2129, #2111, #2104, #2085) * [DS] add more box-plot contracts to our langtable * [DS] use @ifsoln to show the word 'teacher', rather than @teacher (closes #2140) * finalize box plots lesson in response to pull request updates (see #2139, #2129)
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lessons/Data-Science/box-plots/langs/en-us/pages/distribution-by-hand.adoc
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= Distribution of a Dataset | ||
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== Family Gatherings by the Numbers | ||
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@vspace{1ex} | ||
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*Ledet Family Ages*: 1, 44, 3, 42, 46, 74, 75, 21, 74, 70, 40, 41, 45 @right{*Average:* 44.3 years old} | ||
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@n Order the Ages from Least to Greatest: @fitb{}{@ifsoln{1, 3, 21, 40, 41, 42, 44, 45, 46, 70, 74, 74, 75}} | ||
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Then compute: | ||
@fitbruby{5em}{@ifsoln{1}}{Minimum} @hspace{1em} | ||
@fitbruby{5em}{@ifsoln{30.5}}{Q1} @hspace{1em} | ||
@fitbruby{5em}{@ifsoln{44}}{Median} @hspace{1em} | ||
@fitbruby{5em}{@ifsoln{72}}{Q3} @hspace{1em} | ||
@fitbruby{5em}{@ifsoln{75}}{Maximum} @hspace{5em} | ||
@fitbruby{5em}{@ifsoln{74}}{Range} @hspace{1em} @fitbruby{10em}{@ifsoln{41.5}}{Interquartile Range (IQR)} | ||
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@vspace{2ex} | ||
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*Watson Family Ages:* 70, 68, 69, 72, 65, 75, 65, 78, 70, 72, 71, 70 @right{*Average:* 70.4 years old} | ||
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@n Order the Ages from Least to Greatest: @fitb{}{@ifsoln{65, 65, 68, 69, 70, 70, 70, 71, 72, 72, 75, 78}} | ||
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Then compute: | ||
@fitbruby{5em}{@ifsoln{65}}{Minimum} @hspace{1em} | ||
@fitbruby{5em}{@ifsoln{68.5}}{Q1} @hspace{1em} | ||
@fitbruby{5em}{@ifsoln{70}}{Median} @hspace{1em} | ||
@fitbruby{5em}{@ifsoln{72}}{Q3} @hspace{1em} | ||
@fitbruby{5em}{@ifsoln{78}}{Maximum} @hspace{5em} | ||
@fitbruby{5em}{@ifsoln{10}}{Range} @hspace{1em} @fitbruby{10em}{@ifsoln{3.5}}{Interquartile Range (IQR)} | ||
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== Box Plots - Visualizing Shape | ||
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Make box plots to each family's age distribution on the number lines below. Hint: Plot the 5-Number Summaries, draw a box around the IQR (from Q1 to Q3), let the median split the box into 2 parts, and add whiskers from the box to the minimum and maximum values. | ||
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@n Ledet: @ifnotsoln{@image{../images/blank-0to80-num-line-numbered.png}} @ifsoln{@image{../images/ledet.png}} | ||
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@n Watson: @ifnotsoln{@image{../images/blank-0to80-num-line-numbered.png}} @ifsoln{@image{../images/watson.png}} | ||
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== Compare and Contrast | ||
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@n For which family gathering was the average age more typical? How do you know? @fitb{}{@ifsoln{Watson. Because the data is more closely clustered.}} | ||
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@fitb{}{@ifsoln{The Range and IQR are significantly smaller. The mean and median are much more similar.}} | ||
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@n What else do you Notice and Wonder about the data from these two family gatherings? | ||
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@fitb{}{@ifsoln{Answers will vary.}} | ||
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@fitb{}{@ifsoln{The ages for the oldest quarter of the families fall within about the same interval.}} | ||
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@fitb{}{@ifsoln{The minimum age for the Watson family is significantly higher than the median age for the Ledet family.}} | ||
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@n We plotted both of these box plots on number lines with the same scale. Did that make sense? | ||
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@fitb{}{@ifsoln{Yes. Seeing both box plots on the same scale definitely makes them easier to compare,}} | ||
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@fitb{}{@ifsoln{but it might be easier to read the precise values for the Watson family data if we zoomed in on the range the data actually falls within.}} |
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