BoxandWhisker Plots Making and Interpreting BoxandWhisker Plots You

Box-and-Whisker Plots Making and Interpreting Box-and-Whisker Plots

You will: Construct and Interpret Box and Whisker Plots

What is a Box-and Whisker Plot? • Suppose you have a large set of data and want to know how it is distributed. • Think of a teacher’s class set of test scores. • A box-and-whisker plot displays the median, the quartiles, and the greatest and least values.

Why use a Box-and Whisker Plot? • The box-and-whisker plot is a visual way to show the data. • The median and quartiles can easily be read. • The shape of the box and the whiskers gives information about how the numbers are spread out.

Who uses Box-and Whisker Plots? • Scientists who perform experiments display their results using box-andwhisker plots. • Medical researchers display their findings using box-and-whisker plots. • Anyone who reads a scientific report needs to understand how a box-andwhisker works.

We will make a Box-and Whisker Plot Here all of the test scores from your class on the last math test. (Not really!) 87 75 83 94 100 74 68 98 99 85 83 100 72 68 100

You will need a five-number summary in order to construct the box-andwhisker plot. Minimum Lower quartile (Q 1) Median (Q 2) Upper quartile (Q 3) Maximum ? ? ?

Step 1: Write the data in order from least to greatest. 87 75 83 94 100 74 68 98 99 85 83 100 72 68 100 68, 72, 74, 75, 83, 85, 87, 94, 98, 99, 100, 100

Step 2: Find the minimum and maximum values of the data. 68, 72, 74, 75, 83, 85, 87, 94, 98, 99, 100, 100 minimum maximum The minimum is 68. The maximum is 100.

Tell your neighbor how to find the minimum and maximum. To find the minimum. . . To find the maximum. . .

Step 3: Find the median of the data. 68, 72, 74, 75, 83, 85, 87, 94, 98, 99, 100, 100 7 in the lower half 7 in the upper half 1 in the middle The median is 85.

Tell your neighbor how to find the median. To find the median. . .

Step 4: Find the lower quartile (Q 1) of the data. 68, 72, 74, 75, 83, 85, 87, 94, 98, 99, 100, 100 lower half upper half The middle number is not in the lower or upper half.

Step 4: Find the lower quartile (Q 1) of the data. 68, 72, 74, 75, 83, 85, 87, 94, 98, 99, 100, 100 lower half upper half The lower quartile is 74.

Choral Response: What is the lower quartile? The median of the lower half The median of the lower half

Step 5: Find the upper quartile (Q 3) of the data. 68, 72, 74, 75, 83, 85, 87, 94, 98, 99, 100, 100 lower half upper half The middle number is not in the upper or upper half.

Step 5: Find the upper quartile (Q 3) of the data. 68, 72, 74, 75, 83, 85, 87, 94, 98, 99, 100, 100 lower half upper half The upper quartile is 99.

Choral Response: What is the upper quartile? The median of the upper half The median of the upper half

Now that we have our fivenumber summary, we can construct the box-andwhisker plot. Minimum Lower quartile (Q 1) Median (Q 2) Upper quartile (Q 3) Maximum 68 74 85 99 100

Write in Your Notes: What are the five items in the five number summary? I can think of one. . . I bet he knows!

Step 6: Draw a number line that can show the data. 68, 72, 74, 75, 83, 85, 87, 94, 98, 99, 100, 100 50 60 70 80 90 100

Step 7: Mark the minimum, maximum, median and both quartiles on the number line. Minimum Lower quartile (Q 1) Median (Q 2) Upper quartile (Q 3) Maximum 50 60 70 80 68 74 85 99 100 90 100

Step 8: Draw a box between the lower and upper quartiles. Minimum Lower quartile (Q 1) Median (Q 2) Upper quartile (Q 3) Maximum 50 60 68 74 85 99 100 70 80 90 100

Step 9: Draw a vertical line through the median. Minimum Lower quartile (Q 1) Median (Q 2) Upper quartile (Q 3) Maximum 50 60 68 74 85 99 100 70 80 90 100

Step 10: Draw two “whiskers” from the quartiles to the minimum and maximum. Minimum Lower quartile (Q 1) Median (Q 2) Upper quartile (Q 3) Maximum 50 60 68 74 85 99 100 70 80 90 100

Interpreting the box-andwhisker plot 25% 50 60 70 25% 80 25% 90 Remember these are test scores. 25% of the test scores are in each whisker and each section of the box. 25% 100

Find the false statement. 74 68 50 60 70 85 80 90 A) One fourth of the test scores were between 85 and 99. B) One half of the test scores were between 74 and 99. C) One half of the test scores were between 85 and 100. D) Three fourths of the test scores were between 68 and 85. 99 100

Make another box-andwhisker plot from this data: Age at First Inauguration of American Presidents from 1900 to 1999 4 5 6 2 3 6 1 1 1 2 4 4 5 5 6 6 0 1 2 4 9 4 2 is 42 years

Minimum and Maximum Age at First Inauguration of American Presidents from 1900 to 1999 4 5 6 2 3 6 42 is the minimum 1 1 1 2 4 4 5 5 6 6 0 1 2 4 9 4 2 is 42 years 69 is the maximum

What is many Median How halfway What is data items between Age at First Inauguration ofof 18? half are there? American Presidents from 1900 to 1999 54 and 55? 4 5 6 2 3 6 1 1 1 2 4 4 ? 5 5 6 6 0 1 2 4 9 4 2 is 42 years 18 items 54. 5 is the 9 10 median item th th

How many Lower Quartile items Whichare item 9 isitems in the lower in the th The 5 item Age at First Inauguration of half? middle? American Presidents from 1900 to 1999 4 5 6 2 3 6 1 1 1 2 4 4 5 5 6 6 0 1 2 4 9 54. 5 4 2 is 42 years 51 is the lower quartile

How many Upper Quartile items Whichare item 9 isitems in the upper in the th The 5 item Age at First Inauguration of half? middle? American Presidents from 1900 to 1999 4 5 6 2 3 6 1 1 1 2 4 4 5 5 6 6 0 1 2 4 9 54. 5 4 2 is 42 years 60 is the upper quartile

The Box-and-Whisker Plot Age at First Inauguration of American Presidents from 1900 to 1999 4 5 6 54. 5 2 3 6 1 1 1 2 4 4 5 5 6 6 0 1 2 4 9 4 2 is 42 years 40 50 60 70

Find the false statement. 40 50 60 A) The oldest president at his inauguration was 69. B) One fourth of the presidents were 60 or over when inaugurated. C) One half of the presidents were inaugurated between ages 50 and 60. D) The youngest president to be inaugurated in the 1900 s was 42. 70

Multiple Box-and-Whisker Plots Can Be Used to Compare Data Average Monthly High Temperatures in Anchorage, Alaska 0 10 20 30 40 50 60 70 80 90 100 Average Monthly High Temperatures in Long Beach, California 0 10 20 30 40 50 60 70 80 90 100

Find the false statement. Average Monthly High Temperatures in Anchorage, Alaska 0 10 20 30 40 50 60 70 80 90 100 Average Monthly High Temperatures in Long Beach, California A) The range of average monthly high temperatures is broader in Anchorage than in Long Beach. B) The average monthly high temperatures in Long Beach are warmer than Anchorage. C) Half of the average monthly highs in Long Beach are between 27 and 59 degrees.

In your notes. . . 1. List the five items required for a box-and-whisker plot. 2. Write a short description for each.