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Analysing data

Analysing data. There are 12 pupils in a Year 10 class that have their height (in centimetres) measured by the school nurse. 150, 148, 138, 152, 151, 160, 147, 146, 152, 155, 152, 149. Sam says the average height is 152 cm, but Joe says it is 150 cm. Show how they are both right.

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Analysing data

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  1. Analysing data There are 12 pupils in a Year 10 class that have their height (in centimetres) measured by the school nurse. 150, 148, 138, 152, 151, 160, 147, 146, 152, 155, 152, 149 Sam says the average height is 152cm, but Joe says it is 150cm. Show how they are both right. Jenny says that the average is 150.5cm. Can she be right? Justify your answer. Sam and Jenny claim that the range of the values is 1, but Joe says the range is 22. Explain why Joe is right. What mistake have Sam and Jenny made?

  2. No mean feat A local group of five teenagers always hang around together. They are called the ‘meanies’ and they always wear a whole number positive single digit on the front of their shirts. They also always walk about in numerical order. To keep the gang together, the mean value of their shirts always has to be 5. What different combinations of ‘meanies’ can you find?

  3. Saving the ‘meanies’

  4. A mean trick The ‘meanies’ introduce a new rule banning all combinations whose middle number is not a 6. Which of the ‘meanies’ will survive? The remaining ‘meanies’ introduce another rule that only those combinations with more than one 6 are able to remain. Which of the combinations are left now? A final rule states that all combinations without a range of 6 are banned. How many ‘meanies’ remain? What are they?

  5. Mean what you say Invent your own ‘meanie’ story using a different set of rules and instructions. Using 4 different numbers, can you create a set of instructions that will only leave one possible solution?

  6. Mean, median and mode The five cards shown below have the same mean, median and mode value. Jeff thinks that the missing number is 8 and Polly says the number is 4. Explain who is right. A sixth card is added that increases the mean by 0.5. What is the sixth card? What are the new median and mode values? What is the range? Show your working.

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