MATH 2400 – Ch. 2 Vocabulary Mean: the average of a set of data sum/n Median (M): the midpoint of a distribution when all observations are in order from smallest to largest First Quartile (Q1): The median of the first half of observations Third Quartile (Q3): The median of the last half of observations Five-number Summary: Min, Q1, M, Q3, Max

Box Plots (aka Box and Whisker Plots) A box plot is a graphical way to represent the 5 number summary of a set of data. There is generally an axis included beside the graph.

Box Plots with Calculator -STAT, 1:Edit, enter data into a list. -2nd, QUIT -2nd, STATPLOT, select a plot and hit ENTER -Highlight On -Highlight the 5th Type -Make your Xlist correspond to where you stored your data. -Edit Window include all values in the list (x values) *You can hit TRACE to see the 5 number summary

Spotting Outliers One way to determine the spread of the data is to compute the Inter-Quartile Range (IQR) which is the difference between the 3rd and 1st Quartile IQR = Q3 – Q1 A value might be an outlier if… It is less than Q1-1.5*IQR It is greater than Q3+1.5*IQR

Ex. 1 The following represents the travel times to work for 20 randomly selected New York residents. 10 30 5 25 40 20 10 15 30 20 15 20 85 15 65 15 60 60 40 45 Create a stem plot. Use the stem plot to determine the 5 number summary.

Ex. 2 The following represents the travel times to work of 15 workers surveyed in North Carolina. 5 10 10 10 10 12 15 20 20 25 30 30 40 40 60 Create a box plot. Determine the 5 number summary. Determine if there are any potential outliers.

Variance Finding the variance… Find the mean Find the distance each value is from the mean Square each distance Sum the squared distances Divide by one less than the number of values (n-1)

Standard Deviation The standard deviation (S)is computed by taking the square root of the variance. The standard deviation (S) of a set of values is used more than the IQR to describe the spread of the data. Higher S, more spread of data. Lower S, less spread of data.

5 Number Summary vs x̄ and S x̄ and S are sensitive to extreme observation, so they can be misleading when a distribution is strongly skewed or has outliers. Because the two sides of a skewed distribution have different spreads, no single number describes it well. The 5 number summary does a better job.

5 Number Summary vs x̄ and S The 5 number summary is generally better to use than the mean and standard deviation for describing a skewed distribution. We use the mean and standard deviation for symmetric distributions.

Ex. 3 Choose an appropriate measure to compare the travel times between the North Carolina data and the New York data.