GAC010+Statistic+Project

GAC010 assessment statistic project

Assessment Event 2: Project – Statistics

[40 Marks]

Name : _____________________ Date:_____________________

Student No: _______________

Statistics project

Data set: heights of 20 men in centimetres

170 , 171 , 167 , 169 , 162 , 168 , 167 , 165 , 174 , 157 , 160 , 176 , 172 , 182 , 180 , 167 , 173 , 178 , 174 , 166

Use Excel spreadsheets to assist you in answering these questions.

Your answers should include printouts of the spreadsheet graphs, and descriptions of what they mean.

1. Create a dot plot to see the distribution of the data.

2. List the data in order using the dotplot. [1 mark]

3. What is the range? [1 mark]

4. Plot the data in a histogram, and describe the distribution. [3 marks]

5. Create a cumulative frequency curve (ogive) and describe its shape. [1 mark]

6. Use the ogive to estimate the median and quartiles. [2 marks]

7. What is the inter-quartile range? [1 mark]

8. Draw a box plot.

9. Find the mean and standard deviation (sd). [2 marks]

10.Calculate the Pearson measure of Skewness (modal version), and the [3 marks] Quartile measure of skewness. Are they good indicators of skew in the

data? Give reasons for your answer.

11.Which of the three measures of central tendency (mean, median, mode) [1 mark] is the best choice for this data? Give a reason for your answer.

12.What are (mean – 1 sd) and (mean + 1 sd)? What percentage of the [3 marks] data is between them?

13.What are (mean – 2 sd) and (mean + 2 sd)? What percentage of the [3 marks] data is between them?

GAC010 assessment statistic project

14. What are (mean – 3 sd) and (mean + 3 sd)? What percentage of the [3 marks] Data is between them ?

15. Find the value in the data that is closest to z = 0.5. [2 marks]

16. What percentage of the data are between z = –0.5 and 0.5? [2 marks]

17. Find the range of z-values that describes the middle 50% of the data. [2 marks]

18. If you chose a person from this sample randomly, what is the [2 marks] probability that they would be taller than 1 sd above the mean?

.

Marks will be allocated for project presentation including accurate

printouts (or screen pictures if presented electronically) of the four

relevant spreadsheets, and the clarity and accuracy of responses.

GAC010 assessment statistic project

Solutions and Marking Scale

Assessment Event 2: Project - Statistics

[40 Marks]

1.

2. 157 ,160 ,162 ,165 ,166 ,167 , 167 ,167 ,,168 ,169 ,170 ,171 ,172 ,173 ,174,174 , 176 ,178 ,180 ,182 [ 1 Mark ]

3. Range (182 – 157 ) = 25 [ 1 Mark ]

4. The distribution is roughly symmetrical and has an approximate normal shape. It has a slight skew to the right. Appearance may differ slightly if a different minimum or column width is used. [ 1 Mark ]

5 .

GAC010 assessment statistic project

5. Appearance may differ slightly if a different minimum or column width is used. The curve has an approximate S-shape, typical of a normal distribution. [1 Mark]

6. Median about 170, Q1 about 167 and Q3 about 174-from reading the graph.

[2 Mark ] 7. Interquartile range is about 174 – 167 = 7. However the spreadsheet Median, quartiles makes it 7.75. Accept either. [2 Mark ]

8.

9. Mean 169.9, Standard deviation 6.5 [2 Mark ]

10. Mode = 167 (1), therefore:

Pearson Skewness = (169.9 – 167)/6.5 ≈ 0.446 (1)

Pearson Skewness = (169.9 – 167)/6.5 ≈ 0.446 (1)

GAC010 assessment statistic project

Both measures indicate a positive skew, despite the histogram appearing slightly negatively skewed. (1) [ 3 Mark ]

11. The mean is probably the best choice. It accounts for all the data, which has no extreme values, nor a large skew. [ 1 Mark ]

12. Mean – 1 sd = 163.4, mean + 1 sd = 176.4. 70% of values are in this range.

[ 3 Mark ] 13. Mean – 2 sd = 156.9, mean + 2 sd = 182.9. 100% of values are in this range.

[ 3 Mark ] 14. Mean – 3 sd = 150.4, mean + 3 sd = 189.4. 100% of values are in this range.

[ 3 Mark ] 15. For z = 0.5, the value must be close to 169.9 + 6.5/2 = 173.15.The value is 173

[ 2 Mark ] 16. For z = –0.5 the value is 166.65. There are 9 values, or 45%. [ 2 Mark ]

17. The middle 50% cover 167 to 174. 167 is z = –0.45, and 174 is +0.63. The z-range is 1.08. [ 2 Mark ] 18. Three values or 15%. [2 marks]

8 marks to be allocated (as outlined below) for clarity and accuracy of presentation including presentation / printout of relevant spreadsheets:

1 mark for each spreadsheet (as above) [ 4 Mark ] 3 – 4 marks if report completed to a high standard with spreadsheets, and mathematics clearly [ 4 Mark ] 1 – 2 marks if report completed to a satisfactory standard with diagrams and relevant mathematics incorporated into the report