Representing Measures of Central Tendencies Graphing Statistics

Bar Graphs

This is a bar graph that represents favorite types of movies
  • Graphical display of data using bars of different heights.
  • Used when you have categories for your data
  • Note: bar graphs have space between the bars.

Think about it: How does a bar graph help you find measure of central tendencies?

Histograms

  • Used when you have continuous data (things that change over time)
  • No spaces between bars

Think about it: How does a bar graph help you find measure of central tendencies?

Pie Chart

A chart that uses "pie slices" to show relative sizes of data

Note: Pie charts use percentages instead of raw scores to represent data.

How to make them yourself

Step 1:

Step 2

Step 3

Step 4

Think about it: How does the use of percentages instead of raw data change the way you are looking at your data?

Line plot

A line plot is a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer than 25 numbers. It is a quick, simple way to organize data.

Stem and Leaf Plot

A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

Box and Whiskers Plot

To create a box-and-whisker plot, we start by ordering our data (that is, putting the values) in numerical order, if they aren't ordered already. Then we find the median of our data. The median divides the data into two halves. To divide the data into quarters, we then find the medians of these two halves.

How to Create a Box and Whiskers Plot

Below is an example on how to create a box and whisker plot:

Example 1:

Draw a box-and-whisker plot for the following data set:

4.3, 5.1, 3.9, 4.5, 4.4, 4.9, 5.0, 4.7, 4.1, 4.6, 4.4, 4.3, 4.8, 4.4, 4.2, 4.5, 4.4

Step 1: Order the set of data

3.9, 4.1, 4.2, 4.3, 4.3, 4.4, 4.4, 4.4, 4.4, 4.5, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, 5.1

Step 2: Find the Median (Q2)

The first value I need to find from this ordered list is the median of the entire set. Since there are seventeen values in this list, the ninth value is the middle value of the list, and is therefore my median:

3.9, 4.1, 4.2, 4.3, 4.3, 4.4, 4.4, 4.4, 4.4, 4.5, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, 5.1

The median is Q2 = 4.4

Step 3: Find Q1 (Lower Quartile)

Q1 is the median of the first half of the set of data, not including the median of the whole set (Q2):

First half of data: 3.9, 4.1, 4.2, 4.3, 4.3, 4.4, 4.4, 4.4

Q1= (4.3 + 4.3)/2 = 4.3

Step 4: Find Q3 (Upper Quartile)

Q3 is the median of the last half of the data, not including the median of the whole set (Q2).

Last half: 4.5, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, 5.1

Q3 = (4.7 + 4.8)/2 = 4.75

Step 5: Plotting

Example 2:

If you need more examples, click the following link: https://www.saylor.org/site/wp-content/uploads/2013/09/K12MATH007-Box-and-Whisker-Plots-of-Data-and-Statistics.pdf

Your Turn

Complete the following in your OR notebook (Due at the end of the period on 5/4)

Scatter Plot

Scatter plots are similar to line graphs in that they use horizontal and vertical axes to plot data points. However, they have a very specific purpose. Scatter plots show how much one variable is affected by another. The relationship between two variables is called their correlation .

Positive and Negative Correlation

Positive Correlation:

  • Positive slope
  • As x increases, y increases

Negative Correlation:

  • Negative slope
  • As x increases, y decreases

Best Fit Line (AKA Trend Lines)

The goal of a scatter plot is to make it into a line graph. The way we do that is by creating a best fit line or a trend line. These are a straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points.

The best way to find a best fit line is to connect the highest score (maximum), the lowest score (minimum), and some point in the middle of the score distribution, (median, but not necessarily).

Example 1:

Step 1: Plot points on a coordinate plane

Step 2: Make a Best Fit Line

This chart has a positive correlation, which means its slope will be positive

Step 3: Write the equation of the Best Fit/ Trend Line

Your Turn

Complete the following in your Open Response Notebooks

Credits:

Created with images by sergilucaofa - "leaf nature fractal" • fdecomite - "Soma cubes" • rkit - "sheet holes roller shutter" • andymag - "geometry" • fdecomite - "A Stella Octangula inside a Rhombic Dodecahedron" • stux - "tapestry square district" • rkit - "tissue plastic grey" • McShaman - "City geometry"

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