1. Data and Data Analysis

2. Measures of Central Tendency Used to interpret data by choosing one number to represent all the numbers in the data set.

3. Types of measures of Central Tendency Mean Mean Median Median Mode Mode Range Range Quartiles and Interquartile Range Quartiles and Interquartile Range

4. Mean (Average) The sum of the numbers in a data set divided by how many numbers are in that set. The sum of the numbers in a data set divided by how many numbers are in that set. Ex: Find the mean in the data. Ex: Find the mean in the data. 12, 18, 22, 27, 27, 29, 30, 33, 33, 33, 45

5. Median (Middle) The middle number in a data set when the set is in arranged in order from least to greatest. The middle number in a data set when the set is in arranged in order from least to greatest. Example: Find the Median… Example: Find the Median… 33, 17, 16, 23, 45, 21 First but the data in order from least to greatest. 16, 17, 21, 23, 33, 45 There are 2 numbers in the middle, so to find the median, you need to add the 2 numbers together and divide by 2.

6. Mode (Most) The number that appears most often in a data set. The number that appears most often in a data set. A data set may contain more than one mode. A data set may contain more than one mode. Example: Find the Mode: Example: Find the Mode: 22, 16, 15, 31, 31, 10, 31, 15 The mode is 31.

7. Range The measure of the variability in a data set (how the number vary or change). The measure of the variability in a data set (how the number vary or change). To find the range, calculate the difference between the largest and smallest numbers. To find the range, calculate the difference between the largest and smallest numbers. Example: Find the Range Example: Find the Range 11, 15, 18, 21, 27, 33, 33, 35, 40 40-11=29

8. Quartile and Interquartile Range Quartile Quartile Used in statistics to represent one fourth of the data set. Used in statistics to represent one fourth of the data set. Lower Quartile Lower Quartile The median of the lower half of the data set The median of the lower half of the data set Second Quartile Second Quartile Median of the data set Median of the data set Upper Quartile Upper Quartile The median of the upper half of the data set. The median of the upper half of the data set. Interquartile Range Interquartile Range The difference between the upper quartile and the lower quartile. The difference between the upper quartile and the lower quartile.

9. Quartile Example What are the lower quartile, upper quartile, and interquartile range of the following numbers? What are the lower quartile, upper quartile, and interquartile range of the following numbers? 21, 33, 45, 52, 47, 35, 39, 60, 63, 58, 70, 49 Arrange the numbers from least to greatest to find the medians of the upper and lower halves. Arrange the numbers from least to greatest to find the medians of the upper and lower halves. 21, 33, 35, 39, 45, 47, 49, 52, 58, 60, 63, 70 Lower Quartile: Median 37 Upper Quartile: Median 59 Interquartile Range: 59-37=22

10. Percentiles A measure that tells what percent of the total frequency (the total number of numbers in the data set) is scored at or below that measure. A measure that tells what percent of the total frequency (the total number of numbers in the data set) is scored at or below that measure. To find the percentile of a data set, arrange the data in order from least to greatest. To find the percentile of a data set, arrange the data in order from least to greatest. Compute the index, the position of the percentile in the ordered set, by multiplying the percent by the frequency. Compute the index, the position of the percentile in the ordered set, by multiplying the percent by the frequency. If the product is not an integer, round up. If the product is not an integer, round up.

11. Percentile Example The following list represents the scores that 15 students received on the last science quiz. The following list represents the scores that 15 students received on the last science quiz. 13, 14, 16, 17, 19, 19, 20, 20, 21, 21, 21, 22, 24, 24, 25 If Wilson’s score was at the 93 rd percentile, what score did Wilson receive? If Wilson’s score was at the 93 rd percentile, what score did Wilson receive? Convert 93% to a decimal (0.93) and multiply by the frequency (15). Convert 93% to a decimal (0.93) and multiply by the frequency (15). Since 13.95 is not an integer, round up to 14. Wilson’s score is the 14 th score listed. Therefore, Wilson received a score of 24 on the quiz. Since 13.95 is not an integer, round up to 14. Wilson’s score is the 14 th score listed. Therefore, Wilson received a score of 24 on the quiz.

12. Representing Data Here are the different graphs that can be used to represent data…

13. Types of Data Discrete Data Discrete Data Data that can be counted Data that can be counted Continuous Data Continuous Data Data that are assigned an infinite number of values between whole numbers. Data that are assigned an infinite number of values between whole numbers. The assigned values are approximated. The assigned values are approximated.

14. Bar Graph Used to compare amounts. Used to compare amounts. Uses vertical and horizontal bars to show data. Uses vertical and horizontal bars to show data. Sports Drink Sales ColorNumber Sold Blue170 Orange106 Red145 Purple98

15. Histogram A type of bar graph that is used to show continuous data: A type of bar graph that is used to show continuous data: Bars are always vertical. Bars are always vertical. Bars are always connected to each other. Bars are always connected to each other. The horizontal axis is labeled using intervals. The horizontal axis is labeled using intervals. Theater Arrivals Time2:45 - 2:46 2:47- 2:48 2:49- 2:50 2:51- 2:52 2:53- 2:54 2:55 - 2:56 2:57- 2:58 2:59- 3:00 Number of People 81061815354028

16. Line Graph Useful for showing trends in data over a period of time. Useful for showing trends in data over a period of time. Trend Trend A clear direction or pattern in a graph that suggests how the data values will behave in the future. A clear direction or pattern in a graph that suggests how the data values will behave in the future. Pine Tree Growth Year200120022003200420052006 Height (inches) 62236516169

17. Circle Graph (Pie Chart) Used to show how different parts of a whole compare to one another. Used to show how different parts of a whole compare to one another. Each part can be expressed as a fraction or as a percent. Each part can be expressed as a fraction or as a percent. Shows data from one particular time and does not show trends or changes over a period of time. Shows data from one particular time and does not show trends or changes over a period of time. Favorite Sports SportNumber of Votes Percent Soccer7530% Basketbal l 10040% Volleyball5020% Tennis2510% Total250100%

18. Scatterplot Used to show how closely 2 data sets are related. Used to show how closely 2 data sets are related. Time (min) 12345678910111213141516 Depth of Water (mm) 20374964779010512013715016517819320 9 22 6 240 Water Depth

19. Correlation and Trend Lines When data are plotted in a scatterplot, the closer the points come to forming a straight, slanted line, the stronger the correlation. When data are plotted in a scatterplot, the closer the points come to forming a straight, slanted line, the stronger the correlation. If 2 data sets are correlated, a trend line can be drawn to approximate missing data. If 2 data sets are correlated, a trend line can be drawn to approximate missing data. Has close to the same number of points above and below it. Has close to the same number of points above and below it.