Name: Teacher: Date: Section: Review Packet for Test 8 - Statistics Part I: Measures of CENTER vs. Measures of VARIABILITY Statistical Measures of Center: and. Statistical Measures of Variability: and. Part II: Lesson : Measures of CENTER (16-1) & Lesson : Comparing Measures of Center *Mean = *Median = 1) The following are your test grades for quarters 1 and 2. Determine the mean and median for each quarter, and then determine which measure would be the best measure of center for each quarter. Math Test Scores Quarter 1 = {82, 75, 79, 88} Quarter 2 = {90, 88, 55, 91, 81} Mean Median Best Measure of Center 1
2) Find the mean and median for the data values presented in the following line plot (dot plot). a) Find the mean. b) Find the median. c) Describe which would be the best measure of center. 3) Use the following set: 1, 356 889 1,375 847 1,195 991 a) Find the mean to the nearest tenth. b) Find the median. c) Describe which would be the best measure of center. 2
Part III: Lesson : Measures of VARIABILITY & Lesson : Comparing Measures of Variability *Range = *Interquartile Range (I.Q.R.) = Steps to determining the Range & IQR: 1) Order the data values from least to greatest. 2) Label the Minimum & Maximum You can now find the Range. 3) Find the Median = Quartile 2 (in the middle). 4) Split the data in half. 5) Find the Quartile 1 = Median of the lower half (left side) 6) Find the Quartile 3 = Median of the upper half (right side) You can now find the IQR. 4) Find the Range & IQR for each example below. a) Example with 7 Values (Odd) = Easiest 1, 3, 5, 7, 9, 11, 13 b) Example with 6 Values (Even) = Easy 1, 3, 5, 7, 9, 11 c) Example with 5 Values (Odd) = Getting Harder 1, 3, 5, 7, 9 d) Example with 8 Values (Even) = Hardest 1, 3, 5, 7, 9, 11, 13, 15 3
5) Find the range and the interquartile range (IQR) of the data set. 96.1 55.2 13.5 79.2 46.5 23.5 68.1 39.1 82.2 6) A researcher gave the same quiz to two groups. The dot plots show the times it took the people in each group to finish the quiz. Describe the variability of the samples. Choose the correct answer below. a) The variability of the times for Group R is greater than the variability of the times for Group S. b) The variability of the times for the two groups are about the same. c) The variability of the times for Group S is greater than the variability of the times for Group R. 7) The following box plots show the high temperatures, in degrees Fahrenheit, in two cities over the past 10 days. a) IQR for City 1 = b) IQR for City 2 = c) What might you conclude about the cities based on the IQR? a) The weather pattern in City 1 is more consistent than the weather pattern in City 2. b) The weather pattern in City 2 is more consistent than the weather pattern in City 1. c) The weather patterns in City 1 and City 2 are equally consistent. 4
Part IV: Lesson : Making Inferences Using Multiple Populations 8) The following shows the number of calls two radio shows get each day for a ten day period. The two shows are on at the same time. Make a comparative inference based line plots. What conclusions can be made? a) Which of the following is the best inference based on the median values? a) Radio Show 1 generally receives more calls. b) The radio shows receive similar amounts of calls. c) Radio Show 2 generally receives more calls. b) Which of the following shows the most variability? a) Radio Show 1 has more variability, in terms of the number of calls they received per day. b) The radio shows have a similar amount of variability. c) Radio Show 2 has more variability, in terms of the number of calls they received per day. 5
Part IV: Lesson : Mean Absolute Deviation (M.A.D.) Mean Absolute Deviation = MAD Steps: 1) Calculate the Mean. 2) Find the Absolute Deviations from the Mean Figure out how far each data value is away from the mean. Remember: distances are positive, because they are absolute values! 3) Find the Mean Absolute Deviation The Mean of the distances in step #2. 9) You ask 8 classmates how many pens and pencils they have in their bags. The mean number of pens is 8. The mean number of pencils is also 8. Calculate and compare the mean absolute deviations (MAD) for the number of pens and pencils. Round to the nearest integer as needed. a) The mean absolute deviation (MAD) b) The mean absolute deviation (MAD) for the number of pens = for the number of pencils = c) Which mean absolute deviation (MAD) is greater, the pens or pencils? Explain what this means. 6