Statistics

Graphical Displays

Lesson

The same data set can be drawn in several ways. Each kind of plot emphasizes a different feature.

Histogram

Bars over equal-width bins. The height of each bar is the count of observations in that bin. Good for spotting shape (skew, symmetry) and the modal bin (the tallest bar).

Box plot

Built from the five-number summary: min, Q1, median, Q3, max. The box spans Q1 to Q3 (containing the middle 50% of the data); the line inside is the median; the “whiskers” extend to min and max.

$\text{IQR} = Q_3 - Q_1$ . $\text{Range} = \max - \min$ .

Dot plot

One dot per observation, stacked over the value. Easy to spot mode and small data sets.

Stem-and-leaf

Splits each number into a “stem” (everything but the last digit) and a “leaf” (the last digit). Preserves the actual values while showing shape — best for small-to-medium data sets.

Example: $2 | 0, 3, 5$ means 20, 23, 25.

Worked example — box plot

Box plot: min = 10, Q1 = 15, median = 22, Q3 = 30, max = 40.

\text{IQR} = 30 - 15 = 15

\text{Range} = 40 - 10 = 30

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

\text{Box plot: } Q_1 = 20, \ Q_3 = 35. \ \text{IQR?}

Problem 2

Five-number summary; median?

Problem 3

Dot plot counts. Mode?

Problem 4

Stem-leaf 2|0,3,5. Largest value?

Practice

Standard problems matching the lesson.

Problem 5

Box plot Q1=15, Q3=30. IQR?

Problem 6

Same box plot. Range?

Problem 7

Histogram counts 4,8,6,2. Total?

Problem 8

Modal bin count?

Problem 9

Dot plot 2:4, 3:6, 4:3. Total?

Problem 10

Same dot plot. Mode?

Problem 11

Stem-leaf with 7 leaves. Count?

Problem 12

Median of 7-value stem-leaf?

Problem 13

\text{The median in a box plot is at what percentile?}

Problem 14

Dot plot 1:2, 2:5, 3:3, 4:1, 5:1. Total?

Problem 15

Box plot min=2, max=18. Range?

Problem 16

Stem-leaf 5|1,4; 6|0,0,3,7. Smallest?

Problem 17

Same. Largest?

Problem 18

Test scores Q1=70, Q3=88. IQR?

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

Histogram median bin left edge?

Problem 20

Modal bin left edge?

Problem 21

Stem-leaf range?

Problem 22

Lower whisker length (12 to 18)?

Problem 23

Dot plot 10:5,12:3,15:2. Median?

Problem 24

Upper whisker length (Q3=30, max=50)?

Problem 25

Stem-leaf 6|2,3,5,8; 7|0,1,9. Range?

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