Theory
The principal has ninety seconds
The CampusPulse data is in. The principal will look at the screen-time findings for exactly ninety seconds between meetings.
A table of 60 numbers? Unread. The mean and SD you can now compute? Honest, but faceless.
What survives ninety seconds is a picture. You met two of the right pictures in BCA303 (histogram, scatter): today statistics claims them as its own, teaches you to READ them like an examiner, and adds the missing family member: the box plot.
Theory
Three X-rays of one dataset
Think of charts as X-rays, each exposing one thing:
- Histogram: the data's shape: where values pile up, where they thin out.
- Scatter plot: the relationship: do two measurements move together?
- Box plot: the skeleton: five bones (min, Q1, median, Q3, max) and any loose fragments (outliers) flagged individually.
Same patient, three views: a full diagnosis usually wants more than one.
Theory
Histogram and scatter: the statistics reading
Mechanics were BCA303's job (plt.hist, plt.scatter); the statistical READING is this subject's:
Histogram (one numeric variable, binned): symmetric hump = mean ≈ median; long right tail = right-skewed, mean dragged above median (the screen-time story); two humps = two populations sharing one dataset.
Scatter (two numeric variables): up-right drift = positive correlation, down-right = negative, shapeless cloud = none. Dots far from the cloud = outliers worth a roll-number lookup.
Theory
The box plot: five numbers, one glyph
Sort the data, then find the five-number summary:
Min, Q1, Median, Q3, Max, where Q1 and Q3 are the medians of the lower and upper halves (25th and 75th percentiles).
Draw: a box from Q1 to Q3 (it contains the middle 50%: its width is the interquartile range, IQR), a line inside at the median, and whiskers reaching to the farthest values within 1.5 × IQR of the box. Anything beyond the whiskers is plotted as a dot: an outlier, individually named and shamed.
Theory
Worked: screen time becomes a box
Nine values (sorted): 30, 60, 90, 90, 120, 150, 180, 210, 600.
- Median = 5th value = 120.
- Q1 = median of lower four = (60+90)/2 = 75. Q3 = (180+210)/2 = 195.
- IQR = 195 - 75 = 120. Whisker limit: 195 + 1.5×120 = 375.
- The 600 exceeds 375: drawn as an outlier dot; the upper whisker stops at 210.
One glyph now says: middle half between 75 and 195, centre 120, one flagged extremist.
Quiz
In a box plot, what does the line INSIDE the box mark, and what does the box itself span?
- The median; the box spans Q1 to Q3, holding the middle 50% of the data
- The mean; the box spans min to max
- The mode; the box spans one SD either side of the mean
- The median; the box spans the full range of the data
Show the answer
The median; the box spans Q1 to Q3, holding the middle 50% of the data
The box plot is built ENTIRELY from the five-number summary: the inner line is the median (not the mean: the most-marked error in scripts), and the box runs Q1 to Q3: the interquartile range holding the central half. Min and max live at the whisker tips (when no outliers exist), never as the box edges. SD does not appear anywhere in a box plot.
Think first
Read the skew from the box
A box plot of marks shows: the median line sits close to the BOTTOM of the box, and the upper whisker is much longer than the lower one. Before tapping: is the data left-skewed, right-skewed or symmetric, and would the mean sit above or below the median?
Show the answer
Right-skewed: the upper half of the data stretches farther (long upper whisker, median crowded toward Q1), meaning a tail of high values.
In right skew, the tail drags the mean above the median: the same mean-vs-median signature from the central-tendency lesson, now visible as geometry. Reading skew off a box plot without any numbers is exactly the skill exams draw this figure for.
Watch out
The three reading errors
Calling the box line the mean: it is the median, always.
Calling whisker tips min/max: only true when no outliers exist; with outliers, whiskers stop at the 1.5 × IQR fence and dots carry the extremes.
Histogram vs bar chart, again: binned continuous variable (bars touch) vs separate categories (bars apart): the confusion pair follows you from BCA303 into this exam too.
Theory
The box plot's superpower: comparison
One box plot describes; side-by-side box plots compare: hostellers vs day scholars' screen time as two boxes on one axis shows medians, spreads and outliers in a single glance: the ninety-second principal's chart. In Unit 5, R draws it with one command (boxplot(time ~ type)), and the five-number summary comes free from summary(). The chart you learned to read today is the one you will command R to draw.
Summary
Key takeaways
- Histogram = one variable's shape (skew, humps); scatter = two variables' relationship; box plot = the five-number skeleton.
- Five-number summary: min, Q1, median, Q3, max; IQR = Q3 - Q1 holds the middle 50%.
- Box = Q1 to Q3, inner line = MEDIAN, whiskers reach at most 1.5 × IQR past the box, dots beyond = outliers.
- Median near a box edge + one long whisker = skew; long upper whisker means mean > median.
- Side-by-side box plots are the comparison tool for groups.
- Memory hook: three X-rays: shape, relationship, skeleton.