The double dot plot shows the weekly reading habits of a random sample of 10 students in each of two schools. Compare the samples using measures of centre and variation. Can you determine which school’s students read less? Explain.

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Solution

Step 1:
$Data of school = 0 0 1 2 2 3 3 4 5 5 Mean of school A = 0 + 0 + 1 + 2 + 2 + 3 + 3 + 4 + 5 + 5 \div 10 = 25 \div 10 = 2.5 Variation of school A = {(0 - 2.5)}^{2} + {(0 - 2.5)}^{2} + {(1 - 2.5)}^{2} + {(2 - 2.5)}^{2} + {(2 - 2.5)}^{2} + {(3 - 2.5)}^{2} + {(4 - 2.5)}^{2} + {(4 - 2.5)}^{2} + {(5 - 2.5)}^{2} + {(5 - 2.5)}^{2} \div 10 = {(- 2.5)}^{2} + {(- 2.5)}^{2} + {(- 1.5)}^{2} + {(- 0.5)}^{2} + {(- 0.5)}^{2} + {(0.5)}^{2} + {(0.5)}^{2} + {(- 1.5)}^{2} + {(2.5)}^{2} + {(2.5)}^{2} \div 10 = 6.25 + 6.25 + 2.25 + 0.25 + 0.25 + 0.25 + 0.25 + 2.25 + 6.25 + 6.25 \div 10 = 30.5 \div 10 = 3.05$
Step 2:
$Data of school B = 0 2 3 3 3 4 4 4 5 7 Mean of school B = 0 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 7 \div 10 = 60 \div 10 = 6 Variation of school A = {(0 - 6)}^{2} + ({2 - 6)}^{2} + {(3 - 6)}^{2} + {(3 - 6)}^{2} + {(3 - 6)}^{2} + {(4 - 6)}^{2} + {(4 - 6)}^{2} + {(4 - 6)}^{2} + {(5 - 6)}^{2} + {(7 - 6)}^{2} \div 10 = {(- 6)}^{2} + {(- 4)}^{2} + {(- 3)}^{2} + {(- 3)}^{2} + {(- 3)}^{2} + {(- 2)}^{2} + {(- 0.2)}^{2} + {(- 2)}^{2} + {(- 1)}^{2} + {(1)}^{2} \div 10 = 36 + 16 + 9 + 9 + 9 + 4 + 4 + 4 + 1 \div 10 = 93 \div 10 = 9.3$
Final Answer: According to the data of distribution, school A students are reading less compared to that of school B students.

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