PRE-ALGEBRA. Lesson 12-3 Warm-Up PRE-ALGEBRA Box-and-Whisker Plots (12-3) What is “box-and-...

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PRE-ALGEBRA

Transcript of PRE-ALGEBRA. Lesson 12-3 Warm-Up PRE-ALGEBRA Box-and-Whisker Plots (12-3) What is “box-and-...

PRE-ALGEBRA

PRE-ALGEBRA

Lesson 12-3 Warm-Up

PRE-ALGEBRA

Box-and-Whisker Plots (12-3)

What is “box-and-whisker plot”?

How do you make a box-and-whisker plot?

box-and-whisker plot: shows how data (lists of numbers) are distributed (arranged) on a number line by dividing the data into quartiles (four equal parts, like quarters are 4 equal parts of a dollar) and showing how much data is in each part (the median is the “middle” between the middle two, or second and third, quartiles)

Example: Make a box-and-whisker plot of the following table.

Step 1: Arrange the data in order from least to greatest and find the median [number(s) in the middle]

298, 308, 314, 317, 318, 318, 321, 322, 323, 299326 326 327 333

PRE-ALGEBRA

Box-and-Whisker Plots (12-3)

What is “box-and-whisker plot”?

Step 2: Find the lower quartile (fourth) and upper quartile(fourth) by finding the medians of the lower and upper halves.

298, 308 314 317 318 318 321 322 323 326 326 327 333

median of lower quartile = = 315.5

median of upper quartile = = 326 Step 3: Draw a number line. Mark the highest and lowest values in the data set with points. Also mark the median and the median of the quartiles with points. Draw boxes around the middle two quartiles and “whiskers” from the boxes to the maximum (highest) and minimum (lowest) values.

314 + 3172

326 + 3262

PRE-ALGEBRA

The data below represent in centimeters the wingspans

of captured birds. Make a box-and-whisker plot.

61  35  61  22  33  29  40  62  21  49  72  75  28  21  54

Step 1 Arrange the data in order from least to greatest. Find the median.21 21 22 28 29 33 35 40 49 54 61 61 62 72 75

Step 2  Find the lower quartile and upper quartile, which are the medians of the lower and upper halves.21 21 22 28 29 33 35 40 49 54 61 61 62 72 75lower quartile = 28upper quartile = 61

LESSON 12-3

Additional Examples

Box-and-Whisker Plots

PRE-ALGEBRA

(continued)

LESSON 12-3

Additional Examples

Box-and-Whisker Plots

4. Draw whiskers from the box to the minimum and maximum.

3. Mark the median with a vertical segment.

2. Draw a box from the first to the third quartiles.

1. Mark the minimum and maximum, the median, and the quartiles.

Step 3 Draw a number line.

PRE-ALGEBRA

Box-and-Whisker Plots (12-3)

What can you use a box-and-whisker plot to compare data?

Example: Use box-and-whisker plots to compare the masses of orcas (killer whales) and hippopotami.Orca whale masses (in kilograms): 3,900 2,750 2,600 3,100 4,200 2,600 3,700 3,000 2,200Hippo masses (in kilograms): 1,800 2000 3,000 2,500 3,600 2,700 1,900 3,100 2,300

Step 1: Arrange the data in order from least to greatest and find the median [number(s) in the middle]2,200 2,600 2,600 2,750 3,000 3,100 3,700 3,900 4,200 1,800 1,900 2000 2,300 2,500 2,700 3,000 3,100 3,600

Step 2: Find the lower quartile (fourth) and upper quartile (fourth) by finding the medians of the lower and upper halves.2,200 2,600 2,600 2,750 3,000 3,100 3,700 3,900 4,200 1,800 1,900 2000 2,300 2,500 2,700 3,000 3,100 3,600

median of lower quartile (hippos) = 1,950

median of lower quartile (orcas) = = 2,600

median of upper quartile (orcas) = = 3,800

median of upper quartile (hippos) = = 3,050

3,700 + 3,9002

2,600 + 2,6002

1,900 + 2,0002

3,000 + 3,1002

PRE-ALGEBRA

Box-and-Whisker Plots (12-3)

Step 3: Draw one number line that has a big enough range to cover both sets of data. Then, draw the box and whisker plot for orcas under the number line and the box and whisker plot for hippos below that.

PRE-ALGEBRA

Use box-and-whisker plots to compare test scores from

two math classes.

Class A: 92, 84, 76, 68, 90, 67, 82, 71, 79, 85, 79

Class B: 78, 93, 81, 98, 69, 95, 74, 87, 81, 75, 83

LESSON 12-3

Additional Examples

Box-and-Whisker Plots

3. Draw the second box-and-whisker plot below the first one.

1. Draw a number line for both sets of data. Use the range of data points to choose a scale.

2. Draw the first box-and-whisker plot under the umber line.

PRE-ALGEBRA

Box-and-Whisker Plots (12-3)

What can a box-and-whisker tell you about a set of data?

Example: What conclusions can you draw from the following box-and-whisker plot?   

Analysis: The highest score is 90 and the lowest score is 50. At least half of the score are within 10 points of the median (75). The data is not distributed (spread out) evenly (since the quartiles aren’t evenly spaced), and a fourth of the class scored between 75 and 79 points.  Example: What conclusions can you draw from the following box-and-whisker plots?.       

Analysis: The percent of voters who registered (signed up) to vote stayed close to the same from year to year, since the plot is narrow (not too spread out). The percent who actually voted varied more, but it was always less than the percent who registered to vote, Therefore, you can conclude that there were usually many who were registered didn’t vote.

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Describe the data in the box-and-whisker plot.

The lowest score is 55 and the highest is 85. 25% of the scores are at or below 66 and one fourth of the scores are at or above 80. Half of the scores are at or between 66 and 80 and thus half or more than half of the scores are within 10 points of the median, 76.

LESSON 12-3

Additional Examples

Box-and-Whisker Plots

PRE-ALGEBRA

The plots below compare the percents of students who

were eligible to those that participated in extracurricular activities in

one school from 1992 to 2002. What conclusions can you draw?

About 95% of the students were eligible to participate in extracurricular activities. Around 60% of the students did participate. A little less than two thirds of the eligible students participated in extracurricular activities.

LESSON 12-3

Additional Examples

Box-and-Whisker Plots

PRE-ALGEBRA

Solve.

1. Use the data to make a box-and-whisker plot. Student heights (in.) are: 60, 66, 59, 67, 68, 63, 62, 61, 69, 64, 61.

a. What is the median height?

b. Between what heights do 50% of the students fall?

63 in.

between 61 in. and 67 in.

LESSON 12-3

Box-and-Whisker Plots

Lesson Quiz

PRE-ALGEBRA

2. The box-and-whisker plots below compare prices for the same items at Mary’s Discount Store and Ed’s Clothing. What conclusions can you draw?

Prices at the discount store are more tightly grouped around the median price of $25. Half the items cost from $18 to $45. For less expensive items, there is not much difference in the prices at the two stores. For more expensive items, the discount store offers lower prices.

LESSON 12-3

Lesson Quiz

Box-and-Whisker Plots