Chapter 12 Objectives: SWBAT make and interpret frequency tables and histograms SWBAT find mean, median, mode, and range SWBAT make and interpret box-and- whisker plots SWBAT find quartiles and percentiles

12-2 Frequency and Histograms Objective: SWBAT create and interpret frequency tables and histograms.

12-2 Frequency and Histograms Vocabulary: Frequency Frequency Table Histogram Cumulative Frequency Table

12-2 Frequency and Histograms Vocabulary: Frequency: The number of data values in an interval Frequency Table: Groups a set of data values into intervals and shows the frequency for each interval Histogram: A graph that can display data from a frequency table Cumulative Frequency Table: Shows the number of data values that lie in or below a given interval.

Making a Frequency Table The 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, 15 The 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 2 nd column.

Making a Frequency Table The 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, 15 Homerun Results Home Runs Frequency

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 Histogram The 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 Histogram 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.

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

Is 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 Table The 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 Table 17, 3, 1, 30, 11, 7, 1, 5, 2, 39, 22, 13, 2, 0, 21, 1, 49, 41, 27, 2, 0 Step 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 Table 17, 3, 1, 30, 11, 7, 1, 5, 2, 39, 22, 13, 2, 0, 21, 1, 49, 41, 27, 2, 0 Step 2: Write the intervals in the first column. Record the frequency of each interval in the second column.

Making a Cumulative Frequency Table 17, 3, 1, 30, 11, 7, 1, 5, 2, 39, 22, 13, 2, 0, 21, 1, 49, 41, 27, 2, 0 Step 3: For the 3 rd column, add the frequency of each interval to the frequencies of all the previous intervals

Making a Cumulative Frequency Table 17, 3, 1, 30, 11, 7, 1, 5, 2, 39, 22, 13, 2, 0, 21, 1, 49, 41, 27, 2, 0 Number of Text Messages FrequencyCumulative Frequency = = = =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 IntervalFrequencyCumulative Frequency 0 – – – – 19216

Summary Our objective was to: Create and interpret frequency tables and histograms.

Homework Pg. 343 – odd Pg – 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 Tendency Outlier Mean Median Mode Measure of Dispersion Range of a Set of Data

12-3 Measures of Central Tendency and Dispersion Vocabulary: Measure of Central Tendency: mean, median, and mode Outlier: data value that much greater or less than other values in the set Measure of Dispersion: describes how dispersed or spread out, the values in a data set are Range of a Set of Data: is the difference between the greatest and least data values.

Mean, Median, and Mode

Finding Measures of Central Tendency What are the mean, median, and mode of the bowling scores below? Which measure of centered tendency best describes the scores?

Finding Measures of Central Tendency What are the mean, median, and mode of the bowling scores below? Which measure of centered tendency best describes the scores? Mean: = Median: 104, 104, 104, 109, 113, 117, 136, 189 List data in order = The median of an even number of data values is the mean of the two middle data values.

Finding Measures of Central Tendency What are the mean, median, and mode of the bowling scores below? Which measure of centered tendency best describes the scores? Mode: 104The 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: Median: 109 Mode: 104 Mean

Finding a Data Value Your 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? x = 90Use formula for mean x = x = 360 x = 96 Your 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 Range The 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: Range: 47 – 25 = 22 Mean: = 160/5 = 32

Finding the Range The 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: Range: 36 – 28 = 8 Mean: = 160/5 = 32

Finding the Range The 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 4.2 Stock 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: 8Median: 5Mode: 5Range: 13 If you add 5 to each data value, you get the data set 10, 21, 8, 10, 16. Mean: 13Median: 10Mode: 10Range: 13 Notice 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 Values The 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? AthleteTime (min) Bob50 Carlota20 Juan41 Manuel20 Rosita30 Sonia20 Xavier50

Adding a Constant to Data Values The 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? AthleteTime (min) Bob50 Carlota20 Juan41 Manuel20 Rosita30 Sonia20 Xavier50 Step 1: Find the mean, median, mode, and range for the first week. Mean: Median: 30 Mode: 20 Range: 50 – 20 = 30

Adding a Constant to Data Values The 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? AthleteTime (min) Bob50 Carlota20 Juan41 Manuel20 Rosita30 Sonia20 Xavier50 Step 2: Find the mean, median, mode, and range for the second week. Mean: = 38 Median: = 35Add 5 Mode: = 35 Range: 30Range does not change

You Do!! In the 3 rd week of training, the athletes add 10 min to their training times from the 2 nd week. What are the mean, median, mode, and range of the athletes’ training times for the third week? Mean: 48 Median: 45 Mode: 35 Range: 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 Constant A 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 Constant A 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: = 460 7

Multiplying Data Values by a Constant A 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 Constant A 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) = mode: 479(0.7)= range: 1155(0.7) =

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: $345 Median: $ Mode: $ Range: $866.25

Summary Our Objective was to find: Mean Median Mode Range

Homework Workbook: Pg. 347 – – 27 odd

12-4 Box-and-Whisker Plots Objectives: SWBAT make and interpret box-and-whisker plots SWBAT find quartiles and percentiles

12-4 Box-and-Whisker Plots Vocabulary: Quartile Interquartile Range Box-and-Whisker Plot Percentile Percentile Rank

12-4 Box-and-Whisker Plots Vocabulary: Quartile: Values that divide a data set into 4 equal parts. Interquartile Range: Difference between the 3 rd and 1 st quartiles Box-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 parts Percentile Rank: Percentage of data values that are less than or equal to that value

Quartile The median or 2 nd 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 3 rd and 1 st quartiles.

Quartiles

Summarizing a Data Set What are the minimum, first quartile, median, third quartile, and maximum of the data set below? 125, 80, 140, 135, 126, 140, 350, 75 Step 1: Arrange the data in order from least to greatest. 75, 80, 125, 126, 135, 140, 140, 350

Summarizing a Data Set What are the minimum, first quartile, median, third quartile, and maximum of the data set below? 125, 80, 140, 135, 126, 140, 350, 75 Step 2: Find the minimum, maximum, and median. 75, 80, 125, 126, 135, 140, 140, 350 Median (Q2) = = The minimum is 75. The maximum is 350. The median is

Summarizing a Data Set What are the minimum, first quartile, median, third quartile, and maximum of the data set below? 125, 80, 140, 135, 126, 140, 350, 75 Step 3: Find the first quartile and the third quartile. 75, 80, 125, 126, 135, 140, 140, 350 First Quartile (Q1) = = Third Quartile (Q3) = = 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: 60 1 st quartile: 75 Median: 85 3 rd quartile: 95 Maximum: 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?

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? Step 1: Order the data to find the minimum, maximum, and quartiles Minimum Q1 Median(Q2) Q3 Maximum

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? 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 Plots The 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 Rank Of 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 – 5 all