StatisticsStatistics Unit 5
Example 2 We reviewed the three Measures of Central Tendency: Mean, Median, and Mode. We also looked at one Measure of Dispersion – range. Another Measure of Dispersion is Standard Deviation Standard Deviation is a measure of how the values in a data set vary, or deviate, from the mean. Objective: Students will use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Example 2 Standard deviation is a simple measure of the variability or dispersion of a data set. A low standard deviation indicates that the data points tend to be very close to the same value (the mean). A high standard deviation indicates that the data are “spread out” over a large range of values. Objective: Students will use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Example 3 standard deviation formula: Objective: Students will use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Sigma – represents standard deviation Capital Sigma – represents the sum of a series of numbers. n is the number of values in a data set.
Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 1 x1x – 15 = – 15 = – 15 = – 15 = – 15 = 3.2 (-2.4) 2 = 5.76 (0. 1) 2 = 0.01 (-3.8) 2 = (2.9) 2 = 8.41 (3.2) 2 = 10.24
Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x1
Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x
Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x
Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x
Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x
Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x
Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x
Turn to page 745 and complete the 4 problems at the bottom of the page. Set up a table for each set of data Data Set x1x1
Turn to page 745 and complete the 4 problems at the bottom of the page. Set up a table for each set of data Data Set x1x1
POD - Turn to page 745 and complete problem number 1 at the bottom of the page. Set up a table for each set of data Data Set x1x1
POD - Turn to page 745 and complete problem number 1 at the bottom of the page. Set up a table for each set of data Data Set x1x
Example 4 – Find the measures of central tendency, and the measures of dispersion mean median Mode range standard deviation
x1x1
x1x
x1x
x1x
x1x
x1x /15 = 72.27
x1x /15 = 72.27
Example 4 – Find the measures of central tendency, and the measures of dispersion mean median Mode range standard deviation
Example 5 –Identify the Maximum, Minimum, Upper Quartile, Lower Quartile and the Median. Then create a Box and Whisker Plot Maximum Upper Quartile Median Lower Quartile Minimum
Example 6 – Compute the Interquartile Range (IQR) and then determine if there are any outliers Median + (1.5 x IQR) Median - (1.5 x IQR) Maximum Upper Quartile Median Lower Quartile Minimum All of the data falls between and so there are No Outliers Interquartile Range (IQR) 1.5 x Interquartile Range (IQR)
Homework page 745 Number 2
Summary: Need to be able to find mean median Mode range standard deviation Maximum Upper Quartile Median Lower Quartile Minimum Interquartile Range (IQR) 1.5 x Interquartile Range (IQR) Median + (1.5 x IQR) Median - (1.5 x IQR) Create a Box and Whisker Plot
Example 6 – Number 1
Example 6 – Number 2
Example 6 – Number 3 160
Example 6 – Number 4
Example 6 – Number 5
Example 6 – Number 6
Example 6 – Number 7
Homework page 745 Use the data in question # 4 Data set 1 to find the measures of central tendency, measures of dispersion, upper quartile, lower quartile, minimum, maximum and make a box and whisker plot. Find the interquartile range and determine if there are outliers.
Homework page 745 (using data set 1 from question 4) mean median Mode range standard deviation Maximum Upper Quartile Median Lower Quartile Minimum Interquartile Range (IQR) 1.5 x Interquartile Range (IQR) Median + (1.5 x IQR) Median - (1.5 x IQR) = 16
page 745 data set 1 problem number 4 Data Set x1x
page 745 data set 1 problem number 4 Data Set x1x
Homework page 745 (using data set 1 from question 4) mean median Mode range standard deviation Maximum Upper Quartile Median Lower Quartile Minimum Interquartile Range (IQR) 1.5 x Interquartile Range (IQR) Median + (1.5 x IQR) Median - (1.5 x IQR) = =10 1.5x10= = = 20 All of the data falls between 50 and 20 so there are no outliers.
Homework page 745 (using data set 1 from question 4) Maximum Upper Quartile Median Lower Quartile Minimum
Example of a positively skewed box and whisker plot When the whisker is longer on the positive side we say it is positively skewed.
Example of a negatively skewed box and whisker plot When the whisker is longer on the negative side we say it is negatively skewed.
Special cases Find the mode: 1) 14, 14, 14, 15,15, 15, 16, 16, 16, 18 2)2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8 3) 33, 35, 36, 39, 41, 43, 47
Special Cases Find the median: 1) 12, 14, 14, 15,17, 18, 18, 21, 22, 25 2) 43, 45, 51, 53, 54, 54, 59, 60
POD You are one of the finalists at a science fair. The scores of the other finalists are listed in the table. 1.Write an inequality that represents your possible scores if your percentile is 80. What percent of scores must be less than or equal to your score? What is the total number of finalists scores?
Maximum Upper Median Lower Maximum Summary: In your notes, explain the difference between range and interquartile range.
Maximum Upper Median Lower Minimum If your percentile rank is 80, then your score must be greater than or equal to 90 and less than 94 Or 90 < x < 94 Summary: In your notes, explain the difference between range and interquartile range. 75%100%
Example 9 Turn to page 760 in your textbook. The tables in green are called “Two Way Frequency Tables. Read through Activity 1 and 2 and answer questions 1-10 together with your group. ROUND ALL PERCENTS TO THE NEARES TENTH. Be prepared to make a team sheet for team points. Summary: When your groups finishes, in your notes, explain the difference between range and interquartile range.
Example :90 about 13.3% 2. 12:98 about 12.2% 3. 86:98 about 87.8% 4. 25:103 about 24.3% 5. Martial Arts Champ Story of Love 6. 79:100 79% 7. 55:100 55% 8. 67:100 67% 9. 45:100 45% Summary: When your groups finishes, in your notes, explain the difference between range and interquartile range.
Example a + 0.4b + 0.5c Summary: When your groups finishes, in your notes, explain the difference between range and interquartile range. 0.1(0.79) + 0.4(0.55) + 0.5(0.33) or 46.4%