Curriculum

Course: Mathematics — First Preparatory

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Curriculum

Mathematics — First Preparatory

Unit 1: Numbers

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Unit 2: Algebra

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Unit 3: Statistics

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Unit 4: Geometry

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Text lesson

The Arithmetic Mean

Mathematics — First Preparatory

The Arithmetic Mean

Worked examples

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Find the arithmetic mean of the values 4 12 and 8	Findarithmeticmeanvalues
Solution	The sum of the values is 4 + 7 + 9 + 12 + 8 = 40 and there are 5 values. The mean is 40 ÷ 5 = 8	valuesmean
Example 2	The arithmetic mean of five numbers is 10 and four of them are 8 12 and 11. Find the fifth number	arithmeticmeanfivenumbers
Solution	The sum of the five numbers is 10 × 5 = 50. The sum of the four known numbers is 8 + 9 + 12 + 11 = 40. The fifth number is 50 − 40 = 10	fivenumbersfourknown
Example 3	Find the mean from the frequency table: the value 2 has frequency 3 the value 3 has frequency 4 and the value 4 has frequency 3	Findmeanfrequencytable
Solution	The sum of value × frequency = 2 × 3 + 3 × 4 + 4 × 3 = 6 + 12 + 12 = 30. The total of the frequencies is 3 + 4 + 3 = 10. The mean is 30 ÷ 10 = 3	valuefrequencytotalfrequencies

Comparison aspect	Main idea	Keywords
Example 4	The mean of ten numbers is 15. When one number is removed the mean of the remaining nine numbers becomes 16. What number was removed?	meannumbersnumberremoved
Solution	The sum of the ten numbers is 15 × 10 = 150. The sum of the nine remaining numbers is 16 × 9 = 144. The removed number is 150 − 144 = 6	numbersnineremainingremoved
Example 5 (the hardest)	The mean of six numbers is 12. Two new numbers 10 and 16 are added. Find the new mean	meannumbersaddedFind
Solution	The sum of the six numbers is 12 × 6 = 72. After adding the new numbers the sum is 72 + 10 + 16 = 98 and there are 8 values. The new mean is 98 ÷ 8 = 12.25	numbersAfteraddingvalues

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