Lesson

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

The rules

Vocabulary and n

n = total number of data values = sum of all the frequencies.

Quantitative = numbers you measure or count; qualitative = categories (grades, colors).
Frequency f = how many times a value occurs.
'Most data values' = biggest f; 'fewest' = smallest f.

Grouped frequency distribution (Chung's 5 steps)

Width W = range ÷ number of classes, ALWAYS rounded UP to the next whole number; first class starts at the lowest value.

(1) The number of classes is given.
(2) R = max − min.
(3) W = R ÷ classes → ALWAYS round UP to the next whole number.
(4) First class A to B with A = lowest value, B = A + W; next class starts at B.
(5) Boundaries: subtract 0.5 from each end so no value lands in two classes (7–12 → 6.5–11.5).
Check: same width, no overlap, frequencies add up to n.

Midpoint, relative and cumulative frequency

Cumulative frequency is a running total: the first equals the first f, the last equals n.

Midpoint = (lower + upper) ÷ 2.
Relative frequency = f ÷ n.
Cumulative frequency: add each f to the total so far; the last value must be n.

Traps and calculator keys are on the unit page →

Worked examples (8)

Example 1 · 1.1 #10/11

The 25 members of a psychology class were polled as to the number of siblings in their individual families. Construct a frequency distribution for their responses which are

2 3 1 3 3 5 2 3 3 1 1 4 2 5 4 3 6 5 1 6 2 2 2 1 3

Note: The data above are called quantitative data which are measurable or have a numerical value. Numbers are quantitative data.

Number of siblings	Frequency
1	___
2	___
3	___
4	___
5	___
6	___

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Example 2 · 1.1 #2a0/4

a) How many members have 2 siblings?

Use the frequency distribution table in exercise 1 to answer the questions

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Example 3 · 1.1 #2b0/4

b) How many members have 4 siblings or more?

Use the frequency distribution table in exercise 1 to answer the questions

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Example 4 · 1.1 #30/9

Construct a frequency distribution for the data showing the final course grades for students in a pre-calculus course.

F, A, B, B, C, C, B, C, A, A, C, C, D, C, B, D, C, C, B, C

Note: The data above are called qualitative data which are not measurable. Letters, words, colors, etc… are qualitative data.

Grade	Frequency
A	___
B	___
C	___
D	___
F	___

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Example 5 · 1.1 #4a0/4

a) How many students passed the class?

Use the frequency table in exercise 3 to answer the questions

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Example 6 · 1.1 #4b0/4

b) How many percents passed the class?

Use the frequency table in exercise 3 to answer the questions

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Example 7 · 1.1 #50/18

Organize the data of the heights in inches of commonly grown herbs into a grouped frequency table with six classes.

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

Step 1: Determine the number of classes

Step 2: Find the range R = Largest number – Smallest number

Step 3: Find the width of each class W = R / number of classes. Note: Always round up the value of the width to the next whole number

Step 4: Find the first class interval = A – B

Step 5: Find the second class interval = B – C

Notes: A = Lowest data value, B = A + W and C = B + W

Step 6: Find the third, forth… class following the pattern in step 4 and 5.

Note: To avoid the situation where a data can be placed in both classes, we subtract 0.5 on each end of each interval.

Example: Original interval 7 – 12 → New interval 6.5 – 11.5 after subtracting 0.5 on each end

Original Interval	New Interval	Frequency
___	___	___
___	___	___
___	___	___
___	___	___
___	___	___
___	___	___

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Example 8 · 1.1 #60/16

Use the following data to construct a 4 class grouped frequency distribution. The numbers are test scores.

82 47 75 64 57 82 63 93
76 68 84 54 88 77 79 80
94 92 94 80 94 66 81 67
75 73 66 87 76 45 43 56
57 74 50 78 71 84 59 76

Test Scores (Class)	Number of students (Frequency)
___	___
___	___
___	___
___	___

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