BIVARIATED DATA

1. BIVARIATED DATA One of the variables is classified Independent Variable (IV) and is the variable that does the influencing. In Bivariated Data we investigate the relationship between two variables. The other variable is the Dependent Variable ( DV) and is the variable that has been influenced.

2. Example 1: Classify the following variables as Independent and Dependent. a. The ‘Amount of alcohol consumed’ and ‘Reaction time’. Answer: The ‘Amount of alcohol’ is theIndependent Variable. The ‘Reaction time’ is theDependent Variable. b. The ‘Hours employed per week’ and “Salary’. Answer: The ‘Hours employed per week’ is the Independent Variable. The ‘Salary’ is the Dependent Variable.

3. INVESTIGATING THE RELATIONSHIP BETWEEN TWO CATEGORICAL VARIABLES • To investigate the relationship between two Categorical Variables, we organise them in a Two Way Frequency Table. • In addition we display them in a Segmented- Bar Chart. • For the Segmented- Bar Chart the Frequency is always converted to Percentage Frequency. • The Independent Variable is always placed horizontally and the Dependent Variable vertically.

4. Example : Organise and display the “Attitude to gun control” of 100 people who 62 voted ‘For’ and out of them 32 were ‘Males’. The total number of ‘Females’ were 42.Write a report of your observations. Answer: a. Classify the data as IV and DV. The gender is Independent variable and the attitude is the dependent. b. Organise them on a frequency table and find the values that are missing and the percentage frequency.

5. Frequency table

6. c. Construct the ‘Segmented Bar Chart’ using the information from the ‘frequency table’ Segmented Bar Chart Percentage Frequency 100 for 80 against 60 40 20 0 male female gender

7. Report: From the Frequency table and the Segmented- Bar Chart we conclude that a higher Percentage of Females supported gun control than males, 71.4% to 55.2%. This indicates that a person’s attitude to gun control is related to the gender. Example a : Fill in the entries that are missing in the following table: Year group

8. Answer:‘3-6’, total =70‘Never used’ total = 61‘Often used’ total = 98‘Sometimes used’, ‘11-12’ =18‘Sometimes used’, ‘7-10’= 24‘Often used’, ‘7-10’ = 41‘7-10’, total = 74 Example b: Convert the above Two- Way Frequency table to a Percentage- Frequency Table and construct a Segmented Bar Chart.

9. INVESTIGATING THE RELATIONSHIP BETWEEN A CATEGORICAL AND A NUMERICAL VARIABLE • To investigate the relationship between a Numerical and a Categorical Variable with twocategories, we use Back- to- Back Stem and Leaf Plots. • To investigate the relationship between a Numerical and a Categorical Variable with more than two categories we use Parallel Box Plots.

10. Example 1: The following Stem and Leaf Plot displays the ‘Travel times’ in minutes of destinations A and B.a. Compare and interpret the destinations in terms of centre,mode and shape.b. What is the percentage of travel times, either route, that were more than 60 minutes?

11. Answer : a. The shape of the distribution of ‘route A’ is positively skewed since most (mode) of the travel times are in 30’s and it tails to the right. The shape of the distribution of ‘route B’ is symmetric since most of the travel times are in the middle of the distribution. The Median of ‘route A’ is 36 minutes, whereas the Median of ‘route B’ is 41.5, indicating that it takes longer to travel ‘route B’. b. Percentage of more than 60 minutes = 2 × 100 = 5% 37

12. Example 2: The parallel box plots below show the rare of growth of trees of these three samples. What is the rate of growth and variability of the trees in cold conditions compared to hot and mild? hot conditions mild conditions cold conditions rate of growth (in centimetres per year)

13. Answer: The rate of growth in cold conditions is higher since the median is higher. The variability of the trees in cold conditions is smaller, because the range and IQR is smaller.