Quantitative Data Essential Statistics

Quantitative Data O Review O Quantitative data is any data that produces a measurement or amount of something O Examples: Age, distance traveled, height, weight O Utilizes a variety of graphs O Dot plots O Stem plots O Back to Back Stemplots O Line graphs O Scatterplots O Histograms O Boxplots

Numerical variables O or quantitative O observations or measurements take on numerical values O makes sense to average these values O two types - discrete & continuous

Discrete (numerical) O listable set of values O usually counts of items

Continuous (numerical) O data can take on any values in the domain of the variable O usually measurements of something

Classifying variables by the number of variables in a data set Suppose that the PE coach records the height of each student in his class. Univariate - data that describes a single characteristic of the population This is an example of a univariate data

Classifying variables by the number of variables in a data set Suppose that the PE coach records the height and weight of each student in his class. Bivariate - data that describes two characteristics of the population This is an example of a bivariate data

Classifying variables by the number of variables in a data set Suppose that the PE coach records the height, weight, number of sit-ups, and number of push-ups for each student in his class. Multivariate - data that describes more than two characteristics (beyond the scope of this course) This is an example of a multivariate data

Identify the following variables: 1. the appraised value of homes in Plano 2. the color of cars in the teacher’s lot 3. the number of calculators owned by students at your school 4. the zip code of an individual 5. the amount of time it takes students to drive to school Discrete numerical Continuous numerical Categorical Is money a measurement or a count?

Scatter Plots Time Plots Scatter Plots – Start by placing the explanatory variable on the x-axis, and the response variable on the y-axis. Then plot each point, and look for tendencies. Positive linear correlation, Negative quadratic correlation, ect. Time Plots – Place the time on the x-axis, and the amount of the y-axis. Plot each point and then connect them. We utilize these to analyze trends as well.

Line Graph A line graph: Plots each observation against the time at which it was measured. Always put time on the horizontal axis and the variable you are measuring on the vertical axis. Connect the points by lines to display the change over time.

Creating a line graph O In 2014, an parent in Belton ISD claimed that the number of students going to college each year is not growing with our growing population. Use the follow data to display the changes over time. O The following is the number of students that attended college each given year starting in 2004: 106 (2004), 108 (2005), 99 (2006), 126 (2007), 117 (2008), 138 (2009), 139 (2010), 141 (2011), 138 (2012), and 147 (2013) O Create a line graph for this data.

Our Line Graph Create a table Create the graph Year# in College

Scatterplots O Start by placing the explanatory variable on the x-axis, and the response variable on the y-axis. Then plot each point, and look for tendencies. Positive linear correlation, Negative quadratic correlation, ect

Suppose we found the age and weight of a sample of 10 adults. Create a scatterplot of the data below. Is there any relationship between the age and weight of these adults? Age Wt

Suppose we found the height and weight of a sample of 10 adults. Create a scatterplot of the data below. Is there any relationship between the height and weight of these adults? Ht Wt Is it positive or negative? Weak or strong?

The closer the points in a scatterplot are to a straight line - the stronger the relationship. The farther away from a straight line – the weaker the relationship

positive negativeno Identify as having a positive association, a negative association, or no association. 1. Heights of mothers & heights of their adult daughters + 2. Age of a car in years and its current value 3.Weight of a person and calories consumed 4.Height of a person and the person’s birth month 5.Number of hours spent in safety training and the number of accidents that occur - + NO -

Correlation Coefficient (r)- quantitative O A quantitative assessment of the strength & direction of the linear relationship between bivariate, quantitative data O Pearson’s sample correlation is used most O parameter -  rho) O statistic – r O How do I determine strength?

Moderate Correlation Strong correlation Properties of r (correlation coefficient) O legitimate values of r is [-1,1] No Correlation Weak correlation

Plotting scatter graphs This table shows the temperature on 10 days and the number of ice creams a shop sold. Plot the scatter graph. Temperature (°C) Ice creams sold

Plotting scatter graphs We can use scatter graphs to find out if there is any relationship or correlation between two set of data. Hours watching TV Hours doing homework

Calculate r. Interpret r in context. Speed Limit (mph) Avg. # of accidents (weekly) There is a strong, positive, linear relationship between speed limit and average number of accidents per week.

linear transformationsvalue of r is not changed by any linear transformations x (in mm) y Find r. Change to cm & find r. The correlations are the same. Do the following transformations & calculate r 1) 5(x + 14) 2) (y + 30) ÷ 4

value of r does not depend on which of the two variables is labeled x Switch x & y & find r. The correlations are the same. Type: LinReg L2, L1

non-resistantvalue of r is non-resistant x y Find r. Outliers affect the correlation coefficient

linearlyvalue of r is a measure of the extent to which x & y are linearly related Find the correlation for these points: x Y What does this correlation mean? Sketch the scatterplot definite r = 0, but has a definite relationship!

Correlation does not imply causation