# One Variable Statistics

Unit 1 – Interpreting Graphs and Statistics

Class Notes – Day 4 & 5 - Measures of Spread and Box Plots

I.Definitions:

(1)Min Value (Min):

(2)First Quartile ():

(3) Median (M):

(4) Third Quartile ():

(5) Max Value (Max):

(6) Range:

(7) Interquartile Range (IQR):

(8) Percentile:

(9) Outliers:

(10) Measures of Variation:

(11) Box and Whisker Plot:

II.Problem:

Create a box plot that shows the data for the speeds of the 12 fastest animals.

Animal / Cheetah / Antelope / Wildebeest / Lion / Gazelle / Quarter horse / Elk / Cape hunting dog / Coyote / Gray fox / Hyena / zebra
Speed (mph) / 70 / 61 / 50 / 50 / 50 / 47.5 / 45 / 45 / 43 / 42 / 40 / 40

Source:The World Almanac

1. What is a box plot?
1. Order the data from least to greatest.
1. Determine the quartiles.
1. What is the median for this data?
1. What is the inner quartile range?
1. Determine if there are any outliers.
1. Write the five number summary for the data.
1. Complete the box and Whisker Plot

III.Practice

1) Find the Five-Number Summary and Draw a Box Plot. Determine which scores are outliers.

(1)

(2)Carefully look at this table and think about what “Frequency” means before you make your five-number summary and box plot. Determine which scores are outliers.

Score / 1 / 5 / 6 / 7 / 10 / 12
Frequency / 1 / 4 / 7 / 5 / 2 / 1

IV.Analyzing Box Plots

Maria’s Grades:8, 9, 6, 7, 9, 8, 8, 6, 9, 9,

8, 7, 8, 7, 9, 9, 7, 7, 8, 9

Tran’s Grades:9, 8, 6, 9, 7, 9, 8, 4, 8, 5,

9, 9, 9, 6, 4, 6, 5, 8, 8, 8

Gia’s Grades:8, 9, 9, 9, 6, 9, 8, 6, 8, 6,

8, 8, 8, 6, 6, 6, 3, 8, 8, 9

Jack’s Grades:10, 7, 7, 9, 5, 8, 7, 4, 7, 5,

8, 8, 8, 4, 5, 6, 5, 8, 7

Susan’s Grades:8, 8, 7, 9, 7, 8, 8, 6, 8, 7, 8,

8, 8, 7, 8, 8, 10, 9, 9, 9

1) On the copy of the plots above, draw the box plot for Susan’s grades.

2) Why do the plots for Maria and Tran have no whisker at the upper end?

3) Why is the lower whisker on Gia’s box plot so long? Does this mean there are more grades for Gia in that

whisker than in the shorter whisker?

4) Which distribution is the most symmetric? Which distributions are skewed to the left?

5) Use the box plots to determine which student has the lowest median grade.

6) Use the box plots to determine which students have the smallest and largest interquartile range.

(a) Does the student with the smallest interquartile range also have the smallest range?

(b) Does the student with the largest interquartile range also have the largest range?

V.Homework:

1)

The District of Columbia has a far higher number of physicians per 100,000 residents than does any state. That rate, shown on the box plot above, is 683 physicians per 100,000 residents.

(a) Why might you not want to include the District of Columbia in this data set of the 50 states?

(b) What are the dots on the box plot above?

2)

The box plot above shows the distribution of hot dog prices at Major League Baseball parks.

(a) Is the distribution skewed to the left or to the right, or is it symmetric? Explain your reasoning.

(b) Estimate the five number summary. Explain what each value tells you about hot dogs.

3)(a) Find the range and interquartile range of the following set of values:1, 2, 3, 4, 5, 6, 70

(c) Remove the outlier of 70. Find the range and interquartile range of the new set. Which changed

more?

(d) Why is the interquartile range more informative than the range as a measure of variability?

4)For the data set , (a) find the five number summary and draw a box plot