Warm Up # 3: Answer each question to the best of your knowledge. What is univariate data? What is the purpose of a back to back bar graph? How is a histogram different from a bar graph? What is an interval? What are class mark? What is a frequency distribution? What are the three measures of central tendency? How do you find the mean of a frequency distribution table? What does a stem-n-leaf plot best illustrate?

Measures of Variability Statistics Measures of Variability

Essential Question: What does the measure of variability indicate about a set of data?

Introduction to Links:

Lets Digest: How well did the mean, median, or mode represent the data set we just looked at? What about these two: A = {35, 40, 45} B = {10, 40, 70} Both have the same mean but in one the numbers are “farther” from the mean than in the other

Measures of Variability Describe how much a set of data varies Consistency How strongly data related Example A = {35, 40, 45} B = {10, 40, 70} The mean is not accurate because the 2nd set has more variability.

Main ways to represent variability: Range Box and Whisker Plot Standard Deviation Practice!

Range Difference between the greatest number and the least number in a set. What if I told you a set of data has a range of 127, is that good or bad? You don’t know unless you know more about the data set.

Box and Whisker Plots: Graphical representation of variation Similar to how a Histogram lets us “see” what the average value is without actually knowing what it is. 10 20 30 40 50 60 70 80 90 100 110

Box and Whisker Plots: Median (Q2) Q1 – Median of the lower half Q3 – Median of the upper half Outlier Extreme Value (Lower) EV (Upper) 10 20 30 40 50 60 70 80 90 100 110

Box and Whisker Plot Use to illustrate variability not quantity Show your quartile, min, max, and outliers Your Q1, Q2, Q3 are your quartile Interquartile Range (IQR): Q3 – Q1 Semi-interquartile: IQR/2

Calorie’s from 20 popular cereals: 50 90 100 110 120 125 130 140 155 165 200 210 220 250 260 265 270 300

Calculating Outliers Find your IQR Take your IQR*1.5 Q1 – 1.5IQR A number is an outliers if it is below this Q3 + 1.5 IQR A number is an outliers if it is above this

Now you try: 506 583 612 102 789 881 412 457 814 826 First organize the data in increasing order Find the median Split the data into two sets and find the median of each See if there are any outliers Plot the extreme values

Standard Deviation Numerical Method to show Variability – we see more about Standard Deviation later Describe how much items vary from the mean

Calculating Standard Deviation Find the mean of a given data Subtract the mean from each individual data Then square each result Add all together Then divided by how many they are Take the square root of that number.

Calorie’s from 20 popular cereals: 50 90 100 110 120 125 130 140 155 165 200 210 220 250 260 265 270 300

Now you try: 506 583 612 102 789 881 412 457 814 826

Revisiting the EQ: What does the measure of variability indicate about a set of data?

Practice: Link Sheets