Chapter 12Objectives:

SWBAT make and interpret frequency tables and histograms

SWBAT find mean, median, mode, and rangeSWBAT make and interpret box-and- whisker

plotsSWBAT find quartiles and percentiles

12-2 Frequency and Histograms

Objective: SWBAT create and interpret frequency tables and histograms.

12-2 Frequency and Histograms

Vocabulary:FrequencyFrequency TableHistogramCumulative Frequency Table

12-2 Frequency and HistogramsVocabulary:Frequency:The number of data values in an intervalFrequency Table:Groups a set of data values into intervals and shows

the frequency for each intervalHistogram: A graph that can display data from a frequency tableCumulative Frequency Table:Shows the number of data values that lie in or below

a given interval.

Making a Frequency TableThe number of home runs by the batters in a

local home run derby are listed below. What is a frequency table that represents the data?7, 17, 14, 2, 7, 9, 5, 12, 3, 10, 4, 12, 7, 15The minimum data value is 2 and the maximum is 17. So there are 16 possible values, you can divide these values in 4 intervals of size 4. Then we need to count the number of data values in each interval and list the number in the 2nd column.

Making a Frequency TableThe number of home runs by the batters in a

local home run derby are listed below. What is a frequency table that represents the data?7, 17, 14, 2, 7, 9, 5, 12, 3, 10, 4, 12, 7, 15Homerun Results

Home Runs

Frequency

2-5 4

6-9 4

10-13 3

14-17 3

You Do!

What is the frequency table for the data in the previous example that uses the intervals of 5?7, 17, 14, 2, 7, 9, 5, 12, 3, 10, 4, 12, 7, 15

Making a HistogramThe data below are the numbers of hours per

week a group of students spent watching television. What is a histogram that represents the data?7, 10, 1, 5, 14, 22, 6, 8, 0, 11, 13, 3, 4, 14, 5

Use the intervals from the frequency table for the histogram. Draw a bar for each interval. Make the height of each bar equal to the frequency of its interval. The bars should touch but not overlap. Label each axis.

Making a Histogram7, 10, 1, 5, 14, 22, 6, 8, 0, 11, 13, 3, 4, 14, 5

Use the intervals from the frequency table for the histogram. Draw a bar for each interval. Make the height of each bar equal to the frequency of its interval. The bars should touch but not overlap. Label each axis.

You Do!When finishing times, in seconds, for a race are

shown below. What is a histogram that represents the data?

95, 105, 83, 80, 93, 98, 102, 99, 82, 89, 90, 82, 89

Interpreting Histograms

Interpreting HistogramsIs each histogram uniform, symmetric, or skewed?

You Do!The following set of data shows the numbers of

dollars Jay spent on lunch over the last 2 weeks. Make a histogram of the data. Is the histogram uniform, symmetric, or skewed?

17, 1, 4, 11, 14, 14, 5, 16, 6, 5, 9, 10, 13, 9

Uniform

Cumulative Frequency Table

A cumulative frequency table shows the number of data values that lie in or below a give interval. For example, if the cumulative frequency for the interval 70 – 79 is 20, then there are 20 data values less than or equal to 79.

Making a Cumulative Frequency TableThe numbers of text messages sent on one day

by different students are shown. What is a cumulative frequency table that represents the data?

17, 3, 1, 30, 11, 7, 1, 5, 2, 39, 22, 13, 2, 0, 21, 1, 49, 41, 27, 2, 0

Making a Cumulative Frequency Table17, 3, 1, 30, 11, 7, 1, 5, 2, 39, 22, 13, 2, 0, 21, 1,

49, 41, 27, 2, 0Step 1: Divide the data into intervals. The

minimum is 0 and the maximum is 49. You can divide the data into 5 intervals.

Making a Cumulative Frequency Table17, 3, 1, 30, 11, 7, 1, 5, 2, 39, 22, 13, 2, 0, 21, 1,

49, 41, 27, 2, 0Step 2: Write the intervals in the first column.

Record the frequency of each interval in the second column.

Making a Cumulative Frequency Table17, 3, 1, 30, 11, 7, 1, 5, 2, 39, 22, 13, 2, 0, 21, 1,

49, 41, 27, 2, 0Step 3: For the 3rd column, add the frequency of

each interval to the frequencies of all the previous intervals

Making a Cumulative Frequency Table17, 3, 1, 30, 11, 7, 1, 5, 2, 39, 22, 13, 2, 0, 21, 1,

49, 41, 27, 2, 0Number of Text Messages

Frequency Cumulative Frequency

0-9 11 11

10-19 3 14

20-29 3 17

30-39 2 19

40-49 2 21

11+3=14

14+3=17

17+2=19

19+2=21

You Do!!!What is a cumulative frequency table that

represents the data? 12, 13, 15, 1, 5, 7, 10, 9, 2, 2, 7, 11, 2, 1, 0, 15

Interval Frequency Cumulative Frequency

0 – 4 6 6

5 – 9 4 10

10 – 14 4 14

15 – 19 2 16

Summary

Our objective was to:Create and interpret frequency tables and

histograms.

Homework

Pg. 343 – 3441-15 oddPg. 3451 – 3 all

12-3 Measures of Central Tendency and Dispersion

Objective:SWBAT to find mean, median, mode, and range.

12-3 Measures of Central Tendency and Dispersion

Vocabulary:Measure of Central TendencyOutlierMeanMedianModeMeasure of DispersionRange of a Set of Data

12-3 Measures of Central Tendency and Dispersion

Vocabulary:Measure of Central Tendency: mean, median,

and modeOutlier: data value that much greater or less

than other values in the setMeasure of Dispersion: describes how dispersed

or spread out, the values in a data set areRange of a Set of Data: is the difference between

the greatest and least data values.

Mean, Median, and Mode

Finding Measures of Central TendencyWhat are the mean, median, and mode of the

bowling scores below? Which measure of centered tendency best describes the scores?

Finding Measures of Central TendencyWhat are the mean, median, and mode of the

bowling scores below? Which measure of centered tendency best describes the scores?

Mean: 104+117+104+136+189+109+113+104 = 122

8Median: 104, 104, 104, 109, 113, 117, 136, 189List data in order.109 + 113 = 111 2

The median of an even number of data values is the mean of the two middle data values.

Finding Measures of Central TendencyWhat are the mean, median, and mode of the

bowling scores below? Which measure of centered tendency best describes the scores?

Mode: 104 The mode is the data item that occurs the most times

Because there is an outlier, 189, the median is best measure to describe the scores. The mean, 122, is greater than most of the scores. The mode, 104, is the lowest score. Neither the mean nor the mode describes the data well. The median best describes the data.

You do!!Consider the scores from the previous example, that

do not include the outlier, 189. What are the mean, median, and mode of the scores? Which measure of central tendency best describes the data?

Mean: 112.4Median: 109Mode: 104Mean

Finding a Data ValueYour grades on three exams are 80, 93, and 91. What

grade do you need on the next exam to have an average of 90 on the four exams?

80+93+91+x = 90 Use formula for mean 4264 + x = 90 4 264 + x = 360 x = 96Your grade on the next exam must be 96 for you to have

an average of 90.

You Do!!

The grades in the previous example were 80, 93, and 91. What grade would you need on your next exam of have an average of 88 on the four exams?

88%

Finding the RangeThe closing prices, in dollars, of two socks for

the first five days in February are shown. What are the range and mean of each set of data? Use the results to compare the data sets.

Stock A: 25 30 47 28Range: 47 – 25 = 22Mean: 25 + 30 + 30 + 47 + 28

5= 160/5 = 32

Finding the RangeThe closing prices, in dollars, of two socks for

the first five days in February are shown. What are the range and mean of each set of data? Use the results to compare the data sets.

Stock B: 34 28 31 36 36Range: 36 – 28 = 8Mean: 34 + 28 + 31 + 36 + 31

5= 160/5 = 32

Finding the RangeThe closing prices, in dollars, of two socks for

the first five days in February are shown. What are the range and mean of each set of data? Use the results to compare the data sets.

Both sets of stock prices have a mean of 32. The range of the prices for Stock A is 22, and the range of the prices for Stock B is 8. Both stocks had the same average price during the 5-day period, but the prices for Stock A were more spread out.

You DO!For the same days, the closing prices, in dollars,

of Stock C were 7, 4, 3, 6, and 1. The closing prices, in dollars, of Stock D were 24, 15, 2, 10 and 5. What are the range and mean of each set of data? Use your results to compare Stock C with Stock D.

Stock C: Range: 6; Mean 4.2Stock D: Range: 22; Mean 11.2

Note!!Adding the same amount to each value in a set of data

has special consequences for the mean, median, mode, and range.

Consider the data set 5, 16, 3, 5, 11.Mean: 8 Median: 5 Mode: 5 Range: 13If you add 5 to each data value, you get the data set 10,

21, 8, 10, 16.Mean: 13 Median: 10 Mode: 10 Range: 13Notice that the mean, median, and mode all increased

by 5. The range did not change. For any data set, if you add the same amount k to each item, the mean, median, and mode of the new data set also increase by k. The range does not change.

Adding a Constant to Data ValuesThe table shows the times several athletes spend on a

treadmill each day during the first week of training. The athletes add 5 min to their training times during the second week. What are the mean, median, mode, and range of the times for the second week?

Athlete Time (min)

Bob 50

Carlota 20

Juan 41

Manuel 20

Rosita 30

Sonia 20

Xavier 50

Adding a Constant to Data ValuesThe table shows the times several athletes spend on a

treadmill each day during the first week of training. The athletes add 5 min to their training times during the second week. What are the mean, median, mode, and range of the times for the second week?

Athlete Time (min)Bob 50Carlota 20Juan 41Manuel 20Rosita 30Sonia 20Xavier 50

Step 1: Find the mean, median, mode, and range for the first week. Mean: 20+20+20+30+41+50+50

7Median: 30Mode: 20Range: 50 – 20 = 30

Adding a Constant to Data ValuesThe table shows the times several athletes spend on a

treadmill each day during the first week of training. The athletes add 5 min to their training times during the second week. What are the mean, median, mode, and range of the times for the second week?

Athlete Time (min)Bob 50Carlota 20Juan 41Manuel 20Rosita 30Sonia 20Xavier 50

Step 2: Find the mean, median, mode, and range for the second week. Mean: 33 + 5 = 38Median: 30 + 5 = 35 Add 5 Mode: 20 + 5 = 35Range: 30 Range does not

change

You Do!!In the 3rd week of training, the athletes add 10 min to their training times from the 2nd week. What are the mean, median, mode, and range of the athletes’ training times for the third week?

Mean: 48Median: 45Mode: 35Range: 30

Note!Suppose you multiply each value in a data set by

the same amount k. You can find the mean, median, mode, and range of the new data sat by multiplying the mean, median, mode, and range of the original data set by k.

Multiplying Data Values by a ConstantA store sells seven models of televisions. The regular prices are $144, $479, $379, $1299, $171, $479, and $269. This week the store offers a 30% discount on all televisions. What are the mean, median, mode, and range of the discounted price?

Multiplying Data Values by a ConstantA store sells seven models of televisions. The regular prices are $144, $479, $379, $1299, $171, $479, and $269. This week the store offers a 30% discount on all televisions. What are the mean, median, mode, and range of the discounted price?

Step 1: Find the mean, median, mode, and range of the regular prices.

mean: 144+171+269+379+479+479+1299 = 4607

Multiplying Data Values by a ConstantA store sells seven models of televisions. The regular prices are $144, $479, $379, $1299, $171, $479, and $269. This week the store offers a 30% discount on all televisions. What are the mean, median, mode, and range of the discounted price?

Step 1: Find the mean, median, mode, and range of the regular prices.

median: 379 mode: 479 range: 1299 – 144 = 1155

Multiplying Data Values by a ConstantA store sells seven models of televisions. The regular prices are $144, $479, $379, $1299, $171, $479, and $269. This week the store offers a 30% discount on all televisions. What are the mean, median, mode, and range of the discounted price?

Step 2: Multiply the mean, median, mode, and range in Step 1 by 0.7 to find the mean, median, mode, and range of the discounted prices.

mean: 460(0.7) = 322 median: 379(0.7) = 265.30 mode: 479(0.7)= 335.30 range: 1155(0.7) = 808.50

You Do!The following week the store offers a 25%

discount off the regular prices. What are the mean, median, mode, and range of the discounted prices?

Mean: $345Median: $284.25Mode: $359.25Range: $866.25

Summary

Our Objective was to find:• Mean • Median • Mode • Range

Homework

Workbook:Pg. 347 – 348

1 – 27 odd

12-4 Box-and-Whisker Plots

Objectives: SWBAT make and interpret box-and-whisker

plotsSWBAT find quartiles and percentiles

12-4 Box-and-Whisker Plots

Vocabulary:QuartileInterquartile RangeBox-and-Whisker PlotPercentilePercentile Rank

12-4 Box-and-Whisker PlotsVocabulary:Quartile: Values that divide a data set into 4

equal parts.Interquartile Range: Difference between the 3rd

and 1st quartilesBox-and-Whisker Plot: A graph that summarizes a

set of data by displaying it along a number line.Percentile: Separate data set into 100 equal partsPercentile Rank: Percentage of data values that

are less than or equal to that value

Quartile• The median or 2nd Quartile, Q2, separates the

data into upper and lower halves.• The first Quartile, Q1, is the median of the

lower half of the data.• The third Quartile, Q3, is the median of the

upper half of the data.• The interquartile range is the difference

between the 3rd and 1st quartiles.

Quartiles

Summarizing a Data SetWhat are the minimum, first quartile, median,

third quartile, and maximum of the data set below?

125, 80, 140, 135, 126, 140, 350, 75Step 1: Arrange the data in order from least to

greatest. 75, 80, 125, 126, 135, 140, 140, 350

Summarizing a Data SetWhat are the minimum, first quartile, median,

third quartile, and maximum of the data set below?

125, 80, 140, 135, 126, 140, 350, 75Step 2: Find the minimum, maximum, and

median. 75, 80, 125, 126, 135, 140, 140, 350Median (Q2) = 126 + 135 = 130.5

2The minimum is 75. The maximum is 350. The

median is 130.5.

Summarizing a Data SetWhat are the minimum, first quartile, median,

third quartile, and maximum of the data set below?

125, 80, 140, 135, 126, 140, 350, 75Step 3: Find the first quartile and the third

quartile. 75, 80, 125, 126, 135, 140, 140, 350First Quartile (Q1) = 80 + 125 = 102.5

2Third Quartile (Q3) = 140 + 140 = 140

2

You Do!!!What are the minimum, first quartile, median,

third quartile, and maximum of each data set?a) 95, 85, 75, 85, 65, 60, 100, 105, 75, 85, 75

Minimum: 601st quartile: 75Median: 853rd quartile: 95Maximum: 105

Box and Whisker Plot

Making a Box and Whisker Plot

The table shoes the amount of crops harvested in the U.S. for a certain period. What box-and-whisker plot represents the data?

Year Acres (millions)

0 314

1 321

2 315

3 316

4 314

5 311

Year Acres (millions)

6 307

7 316

8 312

9 314

10 303

Making a Box and Whisker PlotThe table shoes the amount of crops harvested in

the U.S. for a certain period. What box-and-whisker plot represents the data?

Step 1: Order the data to find the minimum, maximum, and quartiles.

303 307 311 312 314 314 314 315 316 316 321

Minimum Q1 Median(Q2) Q3 Maximum

Making a Box and Whisker PlotThe table shoes the amount of crops harvested in

the U.S. for a certain period. What box-and-whisker plot represents the data?

Step 2: Draw the box-and-whisker plot.

You Do!

What box-and-whisker plot represents the following monthly sales, in millions of dollars, of audio devices?

15, 4, 9, 16, 10, 16, 8, 14, 25, 34

Interpreting Box-and-Whisker Plots

Use the box-and-whisker plot. What do the interquartile ranges tell you about the average monthly rainfall for each city?

Interpreting Box-and-Whisker PlotsThe box for Miami is longer, so Miami has the

greater interquartile range. This greater range means the middle 50% of Miami’s monthly rainfall vary more widely than those of New Orleans.

Note!

A percentile separates data set into 100 equal parts.

The percentile rank of data is the percentage of data values that are less than or equal to that value

Finding a Percentile RankOf 25 test scores, eight are less than or equal to 75.

What is the percentile rank of a test score of 75? 8_ Write the ratio of the 25 number of test scores less

than or equal to 75 compared to the total number of test scores.

0.32 = 32% Rewrite Fraction as a percent

The percentile rank of 75 is 32.

You Do!!

Of the 25 scores in the previous example, there are 15 scores less than or equal to 85. What is the percentile rank of 85?

60

Summary

12 – 4 Objectives were to: make and interpret box-and-whisker plots

find quartiles and percentiles

Homework

Workbook • Pages 351 – 352 Problems 1 – 19 odd• Page 3531 – 5 all