Unit 1 Study Guide and Schedule: Statistics DUE DATE: A Day: May nd B Day: May 3 rd Name Period Score / Date In-Class Learning Objective In-class Activity Assignment Asgn Done Asgn Late Passed MQ Due Date Apr 18-19 Mean, Median, Mode & Range* Worksheet 1-1 Asgn 1-1 MQ 1-1 Yes / No Apr -3 Apr -3 Make Predictions / Biased & Unbiased Worksheet 1- MQ 1-1 Asgn 1- Apr 4-5 Apr 4-5 Misleading Graphs Worksheet 1-3 Asgn 1-3 Apr 6-9 Apr 6-9 Apr 30- May 1 Box & Whisker Plots* Compare Populations Worksheet 1-4 Asgn 1-4 Worksheet 1-5 MQ 1-4 Asgn 1-5 Finish Study Guide MQ 1-4 Yes / No Apr 30 May 1 May -3 May -3 CRT REVIEW Booklet #1 Booklet #1 May 6-7 May 6-7 CRT REVIEW Booklet # Booklet # May 8-9 May 8-9 CRT REVIEW Booklet #3 Booklet #3 May 10-13 May10-13 CRT REVIEW Surprise PREPARE FOR THE CRT!!!!! *denotes a mastery quiz topic This study guide has 7 problems for you to solve. ******** CRT s are May 14 th -May 17 th ******** Section 1-1: Mean, Median, Mode & Range Textbook Reference: none The Mean is the average. To find the mean, add up all the values in your dataset, then divide that sum by the number of values in your dataset. The Median is the middle value in your dataset. To find the median you need to write down all of your values from least to greatest. o If there are an odd number of values, then the median is the one in the middle. o If there are an even number of values, then you must look at the two middle values. The average of these two numbers is the median. The Mode is the value that occurs most often. If none of the values repeat, then there is no mode. It is also possible for a set to have more than one mode. The Range is simply the difference between the largest and smallest values in your set. In other words, Largest Number Smallest Number = Range Page 1 of 8
Example: Find the mean, median, mode, and range of the following list of values: 14, 9, 18, 13, 6, 14, 10, 1, 0 The Mean There are 9 values in our set so we add them up and divide the sum by 9. (14 + 9 + 18 + 13+ 6 + 14 + 10 + 1 + 0) 9 = 1.9 So the mean is 1.9 The Median First we write our values in order from least to greatest. 6, 9, 10, 1, 13, 14, 14, 18, 0 The median is the value in the middle which is 13. The Mode Since 14 occurs twice while all other values occur only once, the mode is 14. The Range The largest value in the set is 0 and the smallest is 6. Since 0 6 = 14 the range is 14. **If you have a data set with an even amount of data, the method for finding the median is slightly different.** Example: Data set: 1,, 3, 4, 5, 6 *There is no middle number! So we look for the numbers surrounding the middle (3 and 4) and we find the middle of those. To find the middle of 3 and 4, you are just finding the mean so, 3+ 4= 7 and then 7 = 3.5 So the median is 3.5 Section 1-: Make Predictions / Biased & Unbiased Textbook Reference: Book pages 793-808 Making Predications: Statistics The study of collecting, organizing and interpreting date. Survey A question or set of questions designed to collect data about a specific group of people, or population. Population The entire group of items or individuals from which the samples under consideration are taken. Sample- A randomly selected group chosen for the purpose of collecting data. Examples: o The students in Mr. Blackwell s class brought photos from their summer break. The table shows how many students brought each type of photo. Summer Break Photos Location Students Beach 6 Campground 4 Home 7 Theme Park 11 1. What is the probability that a student brought a photo taken at a theme park? number of theme park photos 11 Ptheme ( park) = = number of students with a photo 8 Page of 8
. There are 560 students at the school where Mr. Blackwell teaches. Predict how many students would bring a photo taken at a theme park. 11 s = (S represents the number of theme park photos) 8 560 0 11 s = (Since 8 0 = 560, multiply 11 by 0, and 8 by 0) 0 8 560 0 s = So s = 0 theme park photos 560 560 3. A survey found that 85% of people use emoticons on their instant messengers. Predict how many of the,450 students at Washington Middle School use emoticons. Words: What number of students is 85% of,450 students? Equation: n = 0.85,450 (Percent equation: n represents the number of students) n =, 08.5 (Multiply) About,083 of the students use emoticons. You Try! 1. A survey found that 6 out of every 10 students have a blog. Suppose there are about 50 students at the school. About how many have a blog?. A survey found that 75% of students have cell phones. Predict how many of the 1,900 students at Alice Deal Middle School have cell phones. Unbiased and Biased Samples: Unbiased Sample A sample representative of the entire population. Simple Random Sample An unbiased sample where each item or person in the population is as likely to be chosen as any other. Systematic Random Sample- A sample where the items or people are selected according to a specific time or item interval. Biased Sample - A sample drawn in such a way that one or more parts or the population are favored over others. Convenience Sample A sample which consists of members of a population that are easily accessed. Voluntary Response Sample A sample which involves only those who want to participate in the sampling. Examples: Determine whether each conclusion is valid. Justify your answer. 1. Every tenth person who walks into a department store is surveyed to determine his or her music preference. Out of 150 customers, 70 stated they prefer rock music. The manager concludes that about half of all customers prefer rock music. a. The population is every tenth customer of a department store, so therefore the sample is unbiased, systematic random sample. The conclusion is valid. Page 3 of 8
. The customers of a music store are surveyed to determine their favorite leisure time activity. The results are shown in the graph. The store manager concludes that most people prefer to listen to music in their leisure time. Leisure Time Ac,vi,es Playing sports 0% 6% Other 9% Listening to Music 85% a. The customers at a music store probably like to listen to music in their leisure time. The sample is biased, so the conclusion is not valid. You Try: Determine whether each conclusion is valid. Justify your answer. 1. To determine whether the students will attend the Little Mermaid at the school, Maximus surveys his friends in the play. All of Maximus friends plan to attend. So, Maximus assumes that all the students at his school will also attend.. To determine whether the students at Vista Heights Middle School likes TEAL time. Maximus decides to survey every 10 th students that walks into the front door. Out of 180 students, 100 stated they liked TEAL time. Maximus concludes that about half of all students like TEAL time. Section 1-3: Misleading Graphs Textbook Reference: Book pages 813-80 You see statistics and graphs in newspapers and news reports all of the time. Sometimes, the graphs and statistics can be telling the truth, yet misleading you at the same time. Page 4 of 8
Graphs can mislead you by Using a title that suggests something different than the data. Leaving off the labels or scale. Using a very small scale on the y-axis to make differences look greater. Using very large scale on the y-axis to minimize differences. Beginning the scale at a number other than zero. Using a scale with uneven increments. Using a 3-D design to make it harder to compare bars. Surveying a very small sampling of people. And many other ways. What makes this graph misleading? The height of the cans does show the amount of trash, but the size of the cans increases as well. The larger volume makes up think the value for the year 000 is extraordinarily large compared to 1960. This graph also does not tell how the population has changed from 1960 to 000. Now it s your turn! Which graph is misleading, and why? Page 5 of 8
Statistics can be misleading too. The table shows the quiz grades for Ms. Abney s and Mr. Ochs classes. Ms. Abney s Class Quiz Scores Mr. Ochs Class 10 0 15 0 5 5 5 9 1 6 Ms. Abney claims the average score on a quiz in her class was 5. Mr. Ochs claims the average score on a quiz in his class is 5. How did they arrive at these figures? Are either of them right? For Ms. Abney s classes, 5 is the MODE For Mr. Ochs classes, 5 is the MEDIAN Now it s your turn! Book Sales Per Day 3 18 3 15 4 16 0 11 19 10 13 17 1 3 11 16 36 4 1 7 Find the mean, median, and mode of the data. Which measure of central tendency would be misleading in describing the book sales? Explain. Some information from this section was obtained from: http://www.scholastic.com/teachers/classroom-solutions/011/10/big-ideas-and-new-bookshighlights-ascd-conference Section 1-4: Box & Whisker Plots Textbook Reference: none Here is a set of numbers : 16, 18, 31, 44, 56, 65, 71, 68, 59, 48, 37, 3 First: order the numbers from least to greatest. 16, 18, 3, 31, 37, 44, 48, 56, 59, 65, 68, 71 Second: find the median of the numbers. Since there are 1 numbers then you find the average of the two middle numbers. 44 + 48 = 46 known as the nd quartile or the median. Third: Find the median of the two halves. 16, 18, 3, 31, 37, 44 The median is 3 + 31 = 7 known as the 1 st quartile. 48, 56, 59, 65, 68, 71 The median is 59 + 65 = 6 known as the 3 rd quartile. Page 6 of 8
On a number line (well, just above the number line), mark the lowest number (min.) and the largest number (max.) from our data. Mark the median, 1 st, and 3 rd quartiles. Use the median, 1 st, and 3 rd quartiles to make the box. Then the whiskers go from the box to the minimum and maximum points. Another example: 1, 13, 5, 8, 9, 0, 16, 14, 14, 6, 9, 1, 1 Order from least to greatest 5, 6, 8, 9, 9, 1, 1, 1, 13, 14, 14, 16, 0 Median ( nd quartile) is 1 8+ 9 1 st quartile (median of 1 st half) 5, 6, 8, 9, 9, 1 = 8.5 14 + 14 3 rd quartile (median of nd half) 1, 13, 14, 14, 16, 0 = 14 Draw a number line label the lowest number, highest number, 1 st, nd, and 3 rd quartiles. Use the median, 1 st, and nd quartiles to make the box. Then draw in the whiskers from the box to the minimum and maximum points. Interquartile Range (IQR): The range in between the 1 st and 3 rd quartile. In other words, 3 rd quartile 1 st quartile = interquartile range Section 1-5: Comparing Populations Textbook Reference: Book pages 87-836 Sometimes it s important to compare two different populations and depending on the spread of the data we use different measures of center and variation to compare those sets of data. The following table suggests what should be used in what situation. Ways to Compare Populations If both sets of data are symmetric use: If neither set of data is symmetric use: If only one set of data is symmetric use: To Compare Center Mean Median Median To Compare Variation Distance from each point to the mean Interquartile Range Interquartile Range Page 7 of 8
Example 1: Rebecca surveyed a different group of students in her science and math classes. The following box plots show the results for both classes. Compare their centers and variations. Write an inference you can draw about the two populations. Since neither box plot is symmetric, we should use the median to compare the centers, and the interquartile range to compare the variation. Math Class Science Class Median 10 0 Interquartile Range 0-5=15 5-15=10 The median for the science class is twice the median for math, and there is a greater spread of data around the median for math. Using this information, we can say that overall, the science students posted more blogs than the math students. Now you try it!! 1) The following box plots show the costs of MP3 players at two different stores. Compare the centers and variations of the two populations. Write an inference you can draw about the two populations. Page 8 of 8