Box and Whisker Plot
Box and whisker plots show measure of central tendecy because the box in the plot shows you where 50% of you data is clustered, so you can get an idea about where the majority of you data lies. When making a box and whisker plot all you need is the data set. From there you can plug the values into a calculator and you will be able to find all the information needed to create the plot.
For instance if you had the values 20, 25, 24, 27, 25, 29, and 22. You would then enter these values into you calculator by clicking stat>edit. There is list 1 you would input your data.
From there you would you go to stat>calc> 1-Var Stats. Make sure you're on List 1.
Then you want to find minX which is 20, Q1 which is 22, Med which is 25, Q3 which is 27, and finaly maxX which is 29.
For instance if you had the values 20, 25, 24, 27, 25, 29, and 22. You would then enter these values into you calculator by clicking stat>edit. There is list 1 you would input your data.
From there you would you go to stat>calc> 1-Var Stats. Make sure you're on List 1.
Then you want to find minX which is 20, Q1 which is 22, Med which is 25, Q3 which is 27, and finaly maxX which is 29.
Histograms
Histograms show measures of central tendency by organizing data into bins and showing the frequency of the values. When you have a complete histogram you can see whether it is skewed or symmetric, meaning either the data clusters to the left or right, or the data cluster towards the middle. The x-axis of the graph would show the bin width and the y-axis would show the frequency of the data, how many times each score occurs. The bin width can be found by finding the square root by how many values there are.
Suppose you have the values 13, 25, 16, 20, 3, 6, 11, 21, 15, 8, 20, 24, 27, 12, 13, 17.
There are 16 values so you bin width should be 4.
With this information your histogram should look something like this...
Suppose you have the values 13, 25, 16, 20, 3, 6, 11, 21, 15, 8, 20, 24, 27, 12, 13, 17.
There are 16 values so you bin width should be 4.
With this information your histogram should look something like this...
In this histogram you can see that the data is skewed to the right, which is where the data clusters.
Normal Curve
A normal curve shows measures of central tendency becuase, similar to the box and whisker plot and the histogram, you can see where the majority of the data is clustered. To make a normal curve you need the mean of the data and what one standard deviation would be.
For instance if you had a group of data with the mean of 5 and a standard deviation of 1, remeber to find the standard deviation you follow the steps of finding the minX, Q1, med, ect. for the box and whisker plot, but instead you are looking for the standard deviation (σ).
The curve would look like this
The curve would look like this
68% of the data would be between 4 and 6
95% of the data would be between 3 and 7
99.7% of the data would be between 2 and 8
*Remember that an outlier is three standard deviations plus or minus the mean.*
Outliers for this data would include anything below 2 and above 8.
95% of the data would be between 3 and 7
99.7% of the data would be between 2 and 8
*Remember that an outlier is three standard deviations plus or minus the mean.*
Outliers for this data would include anything below 2 and above 8.