Average The word is often used synonymously with the mean, but it is only Understand the meaning of as a typicality (or location) ‘average’ ‘average’ Spread one type of average. In fact, there are several different types of mean (the one Calculate the mean of a set of data Consistency in this unit properly being named as the mean’). ‘arithmetic Mean NCETM: Bring on the Maths+: Moving on up! Median Statistics: #4 Mode Common approaches Range Every classroom has a set of on the wall Measure Always use brackets when writing out the calculation for a mean, e.g. (2 + 3 + Data 4 + 5) ÷ 4 = 14 ÷ 4 = 3.5 Statistic Statistics Approximate Round Reasoning opportunities and probing questions Suggested activities Possible misconceptions Show me a set of data with a mean (mode, median, range) of 5. KM: If using a calculator some pupils may not use the symbol (or brackets) ‘=’ KM: Always / Sometimes / Never: The mean is greater than the mode for a set correctly; e.g. working out the mean of 2, 3, 4 and 5 as 2 + 3 + 4 + 5 ÷ 4 = KM: of data 10.25. NRICH: Always / Sometimes / Never: The mean is greater than the median for a Some pupils may think that the range is a type of average NRICH: set of data Some pupils may think that a set of data with an even number of items Convince me that a set of data could have more than one mode. has two values for the median, e.g. 2, 4, 5, 6, 7, 8 has a median of 5 and 6 What’s the same and what’s different: mean, mode, median, range? rather than 5.5 Some pupils may not write the data in order before finding the median.
Understand the meaning of ‘average’ as a typicality (or location) Calculate the mean of a set of data Bring on the Maths+: Moving on up! Statistics: #4 Average Spread Consistency Mean Median Mode Range 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’). NCETM: Common approaches Every classroom has a set of on the wall 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 Show me a set of data with a mean (mode, median, range) of 5. Always / Sometimes / Never: The mean is greater than the mode for a set of data Always / Sometimes / Never: The mean is greater than the median for a set of data Convince me that a set of data could have more than one mode. What’s the same and what’s different: mean, mode, median, range? KM: KM: KM: NRICH: NRICH: If using 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 that the range is a type of average Some pupils may think that a set of data with an even number of items has two values for the median, e.g. 2, 4, 5, 6, 7, 8 has a median of 5 and 6 rather than 5.5 Some pupils may not write the data in order before finding the median.
St7_sow.docx