Introducing
Your new presentation assistant.
Refine, enhance, and tailor your content, source relevant images, and edit visuals quicker than ever before.
Trending searches
Scatter Graphs and Cumulative Frequency Curves
What is line of best fit?
It is a straight line that should be drawn from the center of the plotted points on a scatter plot so that is could gather data on two Variables.
Scatter Graphs and Correlation
Correlation
WHAT IS CORRELATION?
trend
strength
Jessica
If there is a correlation between two sets of data, it means they are connected in some way. We have seen that as the temperature increases, the number of ice-creams sold increases. The results are approximately in a straight line, with a positive gradient.
bivariate data: a pair of data
independent variable
dependent variable
How to draw the line of the best fit?
1. Begin by plotting all of your data.
Plotting Scatter Diagrams
Golden Rule:
never use a diagram to make predictions outside of the range of the collected data.
Plotting Diagrams:
Study Hours Regents Score
3 80
5 90
2 75
6 80
7 90
1 50
2 65
7 85
1 40
7 100
Line of Best Fit
3. Place an x (or a + or a dot) in your interpretation of the center of the data on either side of the line.
4. Connect the x marks with a line that extends to the edges of the plot.
Exercises
2. Draw a dotted line that divides the data in two (even numbers of points on either side of the line)
Your x marks may not be in exactly the same place as mine - that's okay, we all see things slightly different. They shouldn't be too far off though.
In this case, there are 21 points on the graph, so, to the best of your ability, draw a line that has approximately 10.5 points on either side of it. There are three points that are really close to the line, so do your best.
Cumulative Frequency Tables and Curves
Length Frequency Cumulative Frequency
21-24 3 3
25-28 7 10 (= 3 + 7)
29-32 12 22 (= 3 + 7 + 12)
33-36 6 28 (= 3 + 7 + 12 + 6)
37-40 4 32 (= 3 + 7 + 12 + 6 + 4)
Sometimes you may be asked questions such as:
- How many people had a mass of less than 50 kilograms?
- How many students scored less than 50% on the test?
Exercise
Cumulative Frequency Tables
Reminder on last time
How many students had a height lower than 160cm?
1
The inter-quartile range is the difference between the lower and upper quartile.
From these values, we can also estimate the inter-quartile range: 33 - 28 = 5.
5
Height, h, cm Frequency
140 < h < 150 1
150 < h < 160 4
160 < h < 170 11
170 < h < 180 7
16
Positions of quartiles:
n/4, n/2, 3n/4
23
Percentiles
large amounts of data
divides data into 100 equal parts
Cumulative Frequency Curves
positions of percentiles: pn/100
Cumulative
Frequency
Height, h, cm Frequency
140 < h < 150 1
150 < h < 160 4
160 < h < 170 11
170 < h < 180 7