Quantitative Data Essential Statistics. Quantitative Data O Review O Quantitative data is any data...
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Transcript of Quantitative Data Essential Statistics. Quantitative Data O Review O Quantitative data is any data...
Quantitative DataEssential Statistics
Quantitative DataO Review
O Quantitative data is any data that produces a measurement or amount of something
O Examples: Age, distance traveled, height, weightO Utilizes a variety of graphs
O Dot plotsO Stem plotsO Back to Back StemplotsO Line graphsO ScatterplotsO HistogramsO Boxplots
Numerical variables
Oor quantitative Oobservations or measurements
take on numerical valuesOmakes sense to average these
valuesOtwo types - discrete &
continuous
Discrete (numerical)
Olistable set of values
Ousually counts of items
Continuous (numerical)
Odata can take on any values in the domain of the variable
Ousually 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
Discrete numerical
Continuous numerical
Categorical
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 GraphA 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 graphO 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 GraphCreate a table Create the graphYear # in
College
2004 106
2005 108
2006 99
2007 126
2008 117
2009 138
2010 139
2011 141
2012 138
2013 147 2004
2006
2008
2010
2012
020406080
100120140160
# of Students in college
# of Stu-dents in col-lege
ScatterplotsOStart 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 24 30 41 28 50 46 49 35 20 39
Wt 256 124 320 185 158 129 103 196 110 130
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 74 65 77 72 68 60 62 73 61 64
Wt 256 124 320 185 158 129 103 196 110 130
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
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)-
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 - r (rho)O statistic – rO How do I determine strength?
Moderate CorrelationStrong correlation
Properties of r(correlation coefficient)
Olegitimate values of r is [-1,1]
0 .5 .8 1-1 -.8 -.5
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
14
10
16
14
20
20
19
22
23
19
21
22
25
30
22
15
18
16
18
19
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 TVHours doing homework
22.5
40.5
3.50.5
22
1.53
2.52
31
50
12
0.53
Calculate r. Interpret r in context.
Speed Limit (mph)
55 50 45 40 30 20
Avg. # of accidents (weekly)
28 25 21 17 11 6
There is a strong, positive, linear relationship between speed limit and average number of accidents per week.
•value of r is not changed by any linear
transformationsx (in mm) 12 15 21 32 26 19 24y 4 7 10 14 9 8 12
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
•value of r is non-resistant
x 12 15 21 32 26 1924
y 4 7 10 14 9 822
Find r.Outliers affect the correlation
coefficient
• value of r is a measure of the extent to which x & y are linearly related
Find the correlation for these points:x -3 -1 1 3 5 7 9Y 40 20 8 4 8 20 40
What does this correlation mean?Sketch the scatterplot
r = 0, but has a definite
relationship!
Correlation does not imply causation
Correlation does not imply causation
Correlation does not imply causation