20 min read

Mean From a Frequency Table

When data is already grouped into a frequency table, each value must be weighted by how often it occurs.

Weighting by Frequency

When data is given as a frequency table, weight each value by how often it occurs: Mean = \frac{\sum ( value \times frequency )}{total frequency} In words: multiply each value by its frequency, add those products, then \div by the total of the frequencies.

Example 1 — mean from a frequency table

Value 2 (frequency 3), value 3 (frequency 5), value 4 (frequency 2). Value Frequency Value \times frequency 23 2 \times 3 = 6 35 3 \times 5 = 15 42 4 \times 2 = 8 Total 1029 Mean = \frac{29}{10} = 2.9 (or 29 \div 10 = 2.9)

Example 2 — cars owned (exam-style)

30 households report cars owned. Frequencies: 0 cars \to 6 homes, 1 car \to 12, 2 cars \to 9, 3 cars \to 3 . Mean = \frac{( 0 \times 6 ) + ( 1 \times 12 ) + ( 2 \times 9 ) + ( 3 \times 3 )}{30} = \frac{0 + 12 + 18 + 9}{30} = \frac{39}{30} = 1.3 Ordered list has 30 values; median is the average of the 15th and 16th. Both fall in the “ 1 car” group, so median = 1 . Mode = 1 (appears most).

Practice

Find the mean of: value 5 (frequency 2), value 6 (frequency 3), value 7 (frequency 5).

Your answer

Weighting by Frequency

When data is given as a frequency table, weight each value by how often it occurs: Mean = \frac{\sum ( value \times frequency )}{total frequency} In words: multiply each value by its frequency, add those products, then \div by the total of the frequencies.

Example 1 — mean from a frequency table

Value 2 (frequency 3), value 3 (frequency 5), value 4 (frequency 2). Value Frequency Value \times frequency 23 2 \times 3 = 6 35 3 \times 5 = 15 42 4 \times 2 = 8 Total 1029 Mean = \frac{29}{10} = 2.9 (or 29 \div 10 = 2.9)

Example 2 — cars owned (exam-style)

30 households report cars owned. Frequencies: 0 cars \to 6 homes, 1 car \to 12, 2 cars \to 9, 3 cars \to 3 . Mean = \frac{( 0 \times 6 ) + ( 1 \times 12 ) + ( 2 \times 9 ) + ( 3 \times 3 )}{30} = \frac{0 + 12 + 18 + 9}{30} = \frac{39}{30} = 1.3 Ordered list has 30 values; median is the average of the 15th and 16th. Both fall in the “ 1 car” group, so median = 1 . Mode = 1 (appears most).

Practice

Find the mean of: value 5 (frequency 2), value 6 (frequency 3), value 7 (frequency 5).

Your answer