Average The word is often used synonymously with the mean, but it is only Approximate a number by rounding to a given number of decimal places ‘average’ Mean one type of average. In fact, there are several different types of mean (the one Measure in this unit properly being named as the mean’). Other types of ‘arithmetic Data average, including the mode and the median, are introduced in later stages. Statistic Statistics NCETM: Approximate Round Common approaches Always use brackets when writing out the calculation for a mean, e.g. (2 + 3 + 4 + 5) ÷ 4 = 14 ÷ 4 = 3.5 Reasoning opportunities and probing questions Suggested activities Possible misconceptions KM: Always / Sometimes / Never: The mean is a whole number. If a calculator some pupils may not use the symbol (or brackets) ‘=’ Kenny is working out the mean of 2, 3, 4 and 5. He calculates 2 + 3 + 4 + 5 correctly; e.g. working out the mean of 2, 3, 4 and 5 as 2 + 3 + 4 + 5 ÷ 4 = ÷ 4 = 10.25. Do you agree with Kenny? Explain your answer. 10.25. NRICH: The average number of children per family (Married Couples, 2012) is 1.8. Some pupils may think the average is always the middle number NCETM: Convince me that this statement makes sense. Some pupils may that the mean must be a whole number Some pupils may not realise that the mean must lie within the range of Learning review NCETM: the data set. KM: NCETM:
Approximate a number by rounding to a given number of decimal places Average Mean Measure Data Statistic Statistics Approximate Round The word ‘average’ is often used synonymously with the mean, but it is only one type of average. In fact, there are several different types of mean (the one in this unit properly being named as the ‘arithmetic mean’). Other types of average, including the mode and the median, are introduced in later stages. NCETM: Common approaches Always use brackets when writing out the calculation for a mean, e.g. (2 + 3 + 4 + 5) ÷ 4 = 14 ÷ 4 = 3.5 Reasoning opportunities and probing questions Suggested activities Possible misconceptions Always / Sometimes / Never: The mean is a whole number. Kenny is working out the mean of 2, 3, 4 and 5. He calculates 2 + 3 + 4 + 5 ÷ 4 = 10.25. Do you agree with Kenny? Explain your answer. The average number of children per family (Married Couples, 2012) is 1.8. Convince me that this statement makes sense. NCETM: KM: NRICH: NCETM: Learning review KM: NCETM: If a calculator some pupils may not use the ‘=’ symbol (or brackets) correctly; e.g. working out the mean of 2, 3, 4 and 5 as 2 + 3 + 4 + 5 ÷ 4 = 10.25. Some pupils may think the average is always the middle number Some pupils may that the mean must be a whole number Some pupils may not realise that the mean must lie within the range of the data set.