MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT A LOOK AT THE OLYMPIC SHOT PUT RESULTS The Olympic Games were first held in 1986 in Athens, Greece. Since then the competition has moved all over the world and over 200 nations participate. There are many different sports to compete in and in this task you will be focusing on shot put results for men and women. The excel spreadsheet contains any information you will need 1. Year the Olympic Game was held 2. The city the Olympic Games was held in. 3. The Gold Medallist Men's Shot Put Throw (metres) 4. The Gold Medallist Women's Shot Put Throw (metres) Note: Women's results are only available from 1948 onwards so there is a blank for the years before 1948. MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT PART ONE: UNIVARIATE DATA FOR MENS SHOT PUT a) Create a stem and leaf plot for the Men's shot put data using the key below. Mens Olympic Shot Put Results in metres Key: 11 2 = 11.2 11 12 13 14 15 16 17 18 19 20 21 22 (2 marks) b) Determine the range for the Men's shot put results. (1 mark) c) Enter the Men's shot put data into your calculator and calculate the 5 figure summary and place values in the table below. Round values to 1 decimal place. Minimum Q1 Median Q3 Maximum (2 marks) d) Conduct an outlier test for the Men's Shot Put results and state if there are any outliers (2 marks) MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT e) Plot a box plot of the Men's Shot Put results on the axes below. Use an appropriate scale. (2 marks) f) Comment the shape of the boxplot (1 mark) g) Calculate the mean and standard deviation for the Men's Shot-Put results and place results in the table below. Round all values to 1 decimal place. Mean Standard Deviation (2 marks) h) Calculate the z-score for Men's Shot Put Result from London (1948) and round to 2 decimal places. (1 mark) i) The z-score for Athens is 0.8. Explain what this result means. (1 mark) j) Which measure of central tendency - mean or median - would be most suitable to describe the Men's Shot put results? Explain your choice. (2 marks) MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT PART TWO: REGRESSION ANALYSIS The table below shows some statistics that have been calculated for this data. Year = (x) Mens Shot Put Result = (y) 1958.43 37.28 18. 57 3.29 0.9583 a) Using the information in the table, show that the equation of the least squares regression line for the men's shot put result ,y, in terms of the Olympic year ,x, is given by = 0.08457x 147 (2 marks) Below is a scatterplot of the Men's Olympic Shot-put results against Year. 25.0 20.0 15.0 Throw (metres) 10.0 5.0 0.0 1880 1900 1920 1940 1960 1980 2000 2020 2040 Year b) Draw the least squares regression line found in part (a) on the scatterplot above. (1 mark) c) Interpret the slope of this least squares regression line in terms of the variables Year and Shot Put Throw (1 mark) MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT d) Explain why it does not make sense to interpret the vertical intercept. (1 mark) e) Calculate the residual values for each Olympic year and place values in the table. Plot the residual plot on the axes below. Year 1896 Residual 1900 1904 1908 1912 1920 1924 1928 1932 Year 1948 1952 1956 1960 1964 1968 1972 1976 1936 Residual Year 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 ( 6 marks) MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT f) Comment on what the residual plot indicates. (1 mark) g) Comment on what the correlation coefficient indicates about the relationship between the Olympic year and Shot put throw distance. (1 mark) h) What percentage of the variation in the shot put throw distance is explained by the variation in the Olympic year? State answer to 2 decimal places. (1 mark) MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT PART THREE: TRANSFORMATIONS In an attempt to improve the linearity of the data, we will look at 3 different transformations. 1 log() 2 a) Apply each of the 3 transformation to your data. Complete the table below for the transformed data values. Use y to represent the shot put throw in metres and x to represent the year in your equations. Round all values to 3 decimals places. Transformation 1 Equation of least squares regression line = log() 2 = 2 = Correlation Coefficient 1 + + + ( 6marks) b) Comment on the improvement or otherwise of each transformation equation over the original equation. Use mathematical reasoning to support your comments. Choose the best equation for calculating predicted values of the four considered (original from (Q2a) plus 3 transformations). (3marks) c) Use your chosen equation to predict the Olympic Shot Put throw in 2020 to 1 decimal place. (1 mark) d) Use your chosen equation to predict the Olympic Shot Put throw in 2032 to 1 decimal place. (1 mark) e) Which prediction from part c) and d) is more reliable. Explain (2 marks) MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT PART FOUR: REGRESSION ANALYSIS WOMENS SHOT PUT Below is a scatterplot of the Women's Shot Put Results against the Olympic Year for the years that the women's event was held. 24.0 22.0 20.0 18.0 16.0 14.0 12.0 10.0 1940 1950 1960 1970 1980 1990 2000 2010 2020 a) Describe the association between the Shot put throw and the Olympic year. (1 mark) b) Perform linear regression analysis and state the least squares regression line for the scatterplot above. Write the equation in the form = + and state values to 3 decimal places. (2 marks) c) Draw the least squares regression line found in part (b) on the scatterplot above. (1 mark) d) Calculate the r value to 3 decimal places. (1 mark) e) Predict the women's shot put throw for the Olympics in 2020. Round your answer to 1 decimal place. (1 mark) f) In the women's shot put data there are a number of outliers that may be affecting the relationship. Remove the data points for the years 2004 and 2008 and recalculate the least squares regression line. State the new equation and correlation coefficient. Round all values to 3 decimal places. (3 marks) MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT g) Compare the two least squares regression line from part (b) and part (f). Which regression line would be best used to make predictions. Explain. (2 marks) PART FIVE: SMOOTHING To improve the linearity of the women's shot put results it is thought best to smooth the data. a) In the table below fill in the shaded cells by completing a 3 point moving mean. Round all values to 1 decimal place. (The outliers at 2004 and 2008 have been removed from the table) Olympic Year 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2012 2016 Women's Shot Put Result 13.8 15.3 16.6 17.3 18.1 19.6 21 21.2 22.4 20.5 22.2 20.6 20.6 20.6 20.7 20.6 3 point moving mean 15.2 18.3 19.6 21.7 21.1 21.1 20.6 20.3 (4marks) b) Calculate the least squares regression line in the form = + for the smoothed data in Q5a) and the r value. Round all values to 3 decimal places. (2 marks) MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT c) Another method of identifying a trend in the data is to graphically smooth the data using a 3 point moving median. Complete this on the graph below. 25.0 20.0 15.0 Womens Shot Put Throw (Metres) 10.0 5.0 0.0 1940 1950 1960 1970 1980 1990 2000 2010 2020 Year (2 marks) d) Comment on the effectiveness of the two smoothing techniques conducted in part (a) and part (c) in revealing the underlying trend of the data. Identify which technique best smoothed this data. (2 marks) MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT PART FIVE (alternative: Deseasonalising Data) The number of hours the Australian Shot put competitor's train each week fluctuates. A 4 week schedule for one competitor is shown below for Monday to Friday. Week 1 Week 2 Week 3 Week 4 Monday 4 5. 5 4.8 5 Tuesday 6.2 6.7 6.0 5.8 Wednesday 3.5 3 2.8 3.8 Thursday 7.1 7.4 7.4 7 Friday 2.8 3.4 4.1 2 a) Plot the data as a time series plot using and explaining an appropriate time code. (2 marks) b) Describe the time series plot in terms of pattern and trend. (1 mark) c) Explain why it would be beneficial to deseasonalise the data (1 mark) MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT A deseasonslised calculation has been started in the tables below. d) Fill in the blank spaces (highlighted grey) to complete the deseasonalisation. Step 1 Week 1 Week 2 Week 3 Week 4 Monday 4 5. 5 4.8 5 Tuesday 6.2 6.7 6.0 5.8 Wednesday 3.5 3 2.8 3.8 Thursday 7.1 7.4 7.4 7 Friday 2.8 3.4 4.1 2 Average 4.72 5.02 (2 marks) Step 2: Round answers to 3 decimal places Monday 0.847 Week 1 Week 2 Week 3 Week 4 Tuesday 1.288 1.195 1.229 0.956 1.059 Wednesday 0.742 0. 577 0.805 Thursday 1.423 1.474 1.483 Friday 0. 593 0.654 0.817 (5 marks) Step 3: Round answers to 2 decimal places Seasonal Indices Monday 0.98 Tuesday Wednesday 0.67 Thursday 1.47 Friday (2 marks) Step 4: Round answers to 1 decimal place. Deseasonalise the original data Week 1 Week 2 Week 3 Week 4 Monday 4.1 5.6 5.1 Tuesday 5.3 4.8 4.6 Wednesday 5.2 4.2 5.7 Thursday 4.8 5.0 5.0 4.8 Friday 4. 5 5. 5 3.2 (4 marks) MAV SACs 2017 CORE: DATA ANALYSIS APPLICATION TASK SHOT PUT e) Add the deseasonalised data to the graph in part (a). Label the new graph. (1 mark) f) Comment on the effectiveness of deseasonalising the data in revealing any underlying trends. (1 mark) g) Determine the equation of the least squares regression line for the deseasonalised data using the least squares regression program on your calculator. Round all values to 3 decimal places. (2 marks) h) Would this least squares regression line be helpful in making future predictions? Explain. (2 marks) Year 1896 1900 1904 1908 1912 1920 1924 1928 1932 1936 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 Country Athens Paris St. Louis London Stockholm Antwerp Paris Amsterdam Los Angeles Berlin London Helsinki Melbourne Rome Tokyo Mexico City Munich Montreal Moscow Los Angeles Seoul Barcelona Atlanta Sydney Athens Beijing London Rio De Janeiro Men Women 11.2 0.0 13.8 0.0 14.8 0.0 14.2 0.0 15.3 0.0 14.8 0.0 15.0 0.0 15.8 0.0 16.0 0.0 16.2 0.0 17.1 13.8 17.4 15.3 18.6 16.6 19.7 17.3 20.3 18.1 20.5 19.6 21.2 21.0 21.1 21.2 21.4 22.4 21.3 20.5 22.5 22.2 21.7 20.6 21.6 20.6 21.4 20.6 21.2 19.6 21.5 19.7 21.9 20.7 22.5 20.6