2. Statistics- a branch of mathematics that involves the study of data The purpose of statistical study is to reach a conclusion or make a decision about an entire group called a population Often it is not possible to survey an entire population. In these cases a sample, or representative part, of the population is used. Once the sample is selected and the data collected, it must be organized. One common way is a frequency table or tally system. Example: SPORTS- In preparing a sports report for the newspaper, Juan recorded the batting averages of 2 baseball players systematically sampled from each of the ten teams in the league. Construct a frequency table for this data..243.281.255.296.278.248.267.303.254.292.304.269.253.241.249.281.277.295.244.294.266.251.270.268.261.302.276.265 The lowest batting average is.241, and the highest is.304. Group the data into intervals. Then mark a tally for each data in the appropriate interval.

3. .243.281.255.296.278.248.267.303.254.292.304.269.253.241.249.281.277.295.244.294.266.251.270.268.261.302.276.265 Batting AverageTallyFrequency.240 -.2495.250 -.2594.260 -.2696.270 -.2794.280 -.2892.290 -.2994.300 -.3093

4. Once data has been organized, it can be analyzed statistically. Three measures of central tendency that can be calculated are the mean, median, and mode. Mean- the sum of the data divided by the number of data. The most representative measure of central tendency for data that does not contain extreme values. Median- the middle value of data when arranged in numerical order. (If the number of data items is even, the median is the average of the two middle numbers) The most representative measure of central tendency for data that contain extreme values. Mode- the number (or numbers) that occurs most often in the set of data. Used to describe the most characteristic value of a set of data. Example: TEST TAKING- The SAT mathematics scores for 8 high school students are listed below. 539541576505548576565558 a.Find the mean of the data b.Find the median of the data c.Find the mode of the data d.Which measure of central tendency is the best indicator of the typical SAT mathematics score for these students?

5. Solution a.To find the mean, add the data and divide by the number of data 539 + 541 + 576 + 505 + 548 + 576 + 565 + 558 8 = 4408 = 551 8 The mean is 551 b. To find the median, first rewrite the data in numerical order 505539541548558565576576 Because there is an even number of data, the median is the average of the two middle numbers 548 + 558 = 1106 = 553 2 2 The median is 553 c. The mode is the number that occurs most often. So the mode is 576 d. The best indicator of the typical SAT mathematics score for the students is the median, 553, which is not affected by the extreme value (505).

7. To construct a stem and leaf plot, first divide each piece of data into two parts: a stem and a leaf The last digit of each number is referred to as its leaf; the remaining digits comprise the stem. The data is organized by grouping together data items that have common stems Example: HEALTH- For an article she was preparing for a women’s magazine, Sharon recorded the cholesterol levels of the twenty women on the magazine staff. 185234208197 259177192188 208200215199 209234208146 216201232186 Cholesterol Levels of Female Staff Members StemsLeaves 14 15 16 17 18 19 20 21 22 23 24 25 Construct a stem-and-Leaf plot to display the data 6 7 5 6 8 2 7 9 0 1 8 8 8 9 5 6 2 4 4 9

8. A histogram is a type of bar graph used to display data. The height of the bars of the graph are used to measure frequency Histograms are frequently used to display data that have been grouped into equal intervals Example: The town newspaper surveyed 40 families, and asked them to record the number Of hours per week their television set was in use. The results are shown in this Frequency table. Construct a histogram to display these data. Number of HoursFrequency 0 – 91 10 – 196 20 -2915 30 – 3912 40 – 492 50 - 594

9. Number of HoursFrequency 0 – 91 10 – 196 20 -2915 30 – 3912 40 – 492 50 - 594 20 18 16 14 12 10 8 6 4 2 0 0-9 10-19 20-29 30-39 40-49 50-59 Frequency Number of Hours Television Use