Statistics and Dispersion: practice questions

6 questions · 11 marks · free, no account · Read the notes first

1. Question 1Multiple choice · 1 mark

   For the data $3, 5, 7, 7, 8$, which of the following is true?

   A

   The mean is greater than the median.

   B

   The mean is 6.

   C

   The mode is 8.

   D

   The median is 5.

2. Question 2Multiple choice · 1 mark

   A set of data has mean 10 and standard deviation 3. Each datum is increased by 5 and then multiplied by 2. Find the new mean and standard deviation.

   A

   mean 25, s.d. 6

   B

   mean 30, s.d. 16

   C

   mean 30, s.d. 6

   D

   mean 20, s.d. 3

3. Question 3Multiple choice · 1 mark

   In a test the mean is 60 and the standard deviation is 8. Find the standard score of a student who scored 72.

   A

   $12$

   B

   $-1.5$

   C

   $0.67$

   D

   $1.5$

4. Question 4Multiple choice · 1 mark

   For a normal distribution, about what percentage of the data lie within 2 standard deviations of the mean?

   A

   68%

   B

   95%

   C

   99.7%

   D

   50%

5. Question 54 marks

   Find the median, the inter-quartile range and the range of the data

   $$2, 4, 4, 5, 7, 8, 9, 12, 13, 16$$
   Show worked solution

   Median $= \dfrac{7 + 8}{2} = 7.5$ 1A

   $Q_1 = 4$ and $Q_3 = 12$ 1M

   Inter-quartile range $= 12 - 4 = 8$ 1A

   Range $= 16 - 2 = 14$ 1A

6. Question 63 marks

   In a Chinese test the mean is 62 and the standard deviation is 10. In a Maths test the mean is 55 and the standard deviation is 15. Mary scored 70 in Chinese and 76 in Maths. In which test did she do relatively better? Explain.

   Show worked solution

   Standard score in Chinese $= \dfrac{70 - 62}{10} = 0.8$ 1A

   Standard score in Maths $= \dfrac{76 - 55}{15} = 1.4$ 1A

   Her standard score is higher in Maths, so she did relatively better in Maths. 1A