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← Unit 4 · Five-number summary & box plots

Lesson

Read the rule, then work each example: try the setup yourself, then tap to check one step at a time.

The rules

Quartiles: leave the median OUT

Sort first. Q1 = middle of the values BEFORE the median, Q3 = middle of the values AFTER it; when n is odd the median is in neither half.

  1. Sort the data (stat → 2:SortA().
  2. Median = middle value (average the two middles if n is even).
  3. n odd → drop the median; n even → split straight down the middle.
  4. Q1 = median of the lower half; Q3 = median of the upper half.
  5. Check against 1-Var Stats: it uses the same rule.

IQR and outlier limits

IQR = Q3 − Q1. Lower limit = Q1 − 1.5·IQR, upper limit = Q3 + 1.5·IQR; an outlier is below the lower or above the upper limit.

  1. Find Q1 and Q3 (median excluded).
  2. IQR = Q3 − Q1.
  3. Multiply: 1.5 × IQR.
  4. Lower limit = Q1 − that; upper limit = Q3 + that.
  5. Any data value outside the limits is an outlier.

Reading a box plot

Left whisker end = Min, box left edge = Q1, line inside = median, right edge = Q3, right whisker end = Max; each section holds 25%.

Traps and calculator keys are on the unit page →

Worked examples (8)

Example 1 · 1.4 #10/9

Find the Five – Number Summary for the heights in inches of commonly grown herbs below

18 20 18 18 24 10 15 12 20 36 14 20 18 24 18 16 16 20 7

Try the setup yourself first, then tap.

Example 2 · 1.4 #20/5

Construct a box plot from the Five-Number Summary in exercise 1.

Try the setup yourself first, then tap.

Example 3 · 1.4 #3a0/4

a) What is the lowest data value?

Use the box plot in exercise 2 to answer the questions

Try the setup yourself first, then tap.

Example 4 · 1.4 #3b0/4

b) What is the median?

Use the box plot in exercise 2 to answer the questions

Try the setup yourself first, then tap.

Example 5 · 1.4 #3c0/4

c) How many percents fall between 15 and 20?

Use the box plot in exercise 2 to answer the questions

Try the setup yourself first, then tap.

Example 6 · 1.4 #4a0/10

a) Find the potential outlier(s)

Step 1: Sort the data in an increasing order, then find the first quartile (Q1) and the third quartile (Q3).

Step 2: Find the Interquartile Range (IQR). IQR = Q3 – Q1

Step 3: Find the lower limit and the upper limit. Lower limit = Q1 – 1.5 IQR, Upper limit = Q3 + 1.5 IQR

Step 4: Find the outlier(s). Note: Outliers are data values smaller than lower limit or bigger than the upper limit.

The weekly TV – viewing times for a sample of 20 people are given in the table below.

25 41 27 32 43
66 35 31 15 5
34 26 32 38 16
30 38 30 20 21

Try the setup yourself first, then tap.

Example 7 · 1.4 #4b0/5

b) Construct a box plot with the outliers

The weekly TV – viewing times for a sample of 20 people are given in the table below.

25 41 27 32 43
66 35 31 15 5
34 26 32 38 16
30 38 30 20 21

Try the setup yourself first, then tap.

Example 8 · 1.4 #4c0/8

c) Construct a box plot without the outliers

The weekly TV – viewing times for a sample of 20 people are given in the table below.

25 41 27 32 43
66 35 31 15 5
34 26 32 38 16
30 38 30 20 21

Try the setup yourself first, then tap.

Practice nowTake the checkpoint