Data Distributions Guided Notes

Data Distributions Guided Notes Questions: Lesson 1: Data Collection and Frequency Tables 1.______students have 1 pet. 2.______students have no pets. Vocabulary: 3.How many more students have 1 pet than have no pets? ______1. Data – ______or ______that are collected 4. The data are organized in the frequency table above. The data 2. Survey – given to investigate ______or ______by show that _____ more students have 1 pet than have no pets. ______a group of people 3. Categorical data – data that is a ______or ______4. Numerical data – data that is a ______Example 2: A survey of 200 people asked “On your dream 5. Population – the ______you want to find information about vacation, how would you get where you are going?” The results 6. Sample – a group of people ______a population are shown in the frequency table: 7. Census – a ______of an entire ______8. Parameter – a measured characteristic of a ______Transportation Number of people 9. Statistic – a measured characteristic of a ______10. Frequency distribution (______table) – a table that Airplane 125 ______data to show ______Automobile 6 ______each item or group of items appears Boat 42 Train 27 Example 1: Maxine took a census of all the students in Ms. Alvarez’s class. The data below show the number of pets owned by each student:

0, 1, 3, 2, 1, 4, 2, 1, 0, 3, 5, 2, 2, 1, 3, 2, 1, 4, 5, 0, 0, 1, 2, 1, 2 1.What percent of those surveyed chose boat?

Organize the data in an ungrouped frequency table. Use the data to 2.What percent did not chose airplane? determine how many more students have 1 pet than have no pets. Lesson 2: Measures of Central Tendency

Vocabulary: # of Tallies Frequency pets 1. Mean – the ______(______up the values and ______by 0 the # of values) 1 2. Median – the ______number in a list of numbers (Hint: write the numbers in ______) 2 3. Mode – the value that occurs the ______3 4

5 Example 1: In Ms. Lin’s 7th grade class, there are 21 people, Step 2: Find the sum if Zack has a mean score of 80 on all 5 including Ms. Lin. There ages are: quizzes.

11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 37 Step 3: What number would you need to add 317 to get a sum of 400? 1.Find the mean, median, and mode

Step 4: Check your answer 2.Analyze the data. Which measure of central tendency would be the most appropriate to use? Example 4: This stem and leaf plot shows the number of miles Jamal biked per week for each of the past 10 weeks: Example 2: Find all measures of central tendency for the data below.

Score Frequency 10 5 9 8 8 10 This week, Jamal was ill so he only biked 11 miles. How does this 7 2 change the median and mean of the data?

1. Find the mean for the 10 weeks before this week. Mean: 2. Now find the mean for all 11 weeks, including this week. Median: 3. How did including the outlier change the mean, if at all? Mode: 4. Find the median for the 10 weeks before this week. Example 3: Zack wants to have a mean score of 80 on his health quizzes. He scored 70, 75, 82, and 90 on his first four quizzes. 5. Now find the median including the 11 miles Jamal biked this week. What score must he earn on his fifth quiz to have a mean score of exactly 80 for all five quizzes? 6. How did including the outlier change the median, if at all? SMART STRATEGY *Including the ______lowers the mean by ______Step 1: Find the sum of the 4 scores you know. miles, but only lowers the median by ______miles. Lesson 3: Measures of Variation You are looking for the following --

Vocabulary: 1. Lower extreme (LE): 2.Quartile 1 (LQ): 1. Variability – How a data set is spread out 3.Median (Q2): 2. Range – The difference between the greatest and least values in 4.Quartile 3 (Q3): a data set 5.Upper Extreme (UE): 3. Quartile - The three numbers that split an ordered data set in 6.Range: four equal groups 7.IQR:

First Quartile – Lesson 4: Box-and-Whisker Plot

Second Quartile – Vocabulary:

Third Quartle – 1. Box-and-Whisker Plot: a way of ______data into ______that is useful for showing data distribution 4. 5 Number Summary – the ______numbers that dived a set of data into ______Steps for creating a box-and-whisker plot:

1. Step 1: Put the data in order from ______to ______2. Step 2: Find the ______3. Step 3: Find the ______4. Step 4: Find the ______5. Step 5: Draw a ______Step 6: Place a ______above the median, lower quartile, and 5. Interquartile range: The ______between the ______and upper quartile ______quartiles. (Note that the first and third quartiles are Step 7: Draw a ______(with a ______line thru the ______) sometimes called upper and lower quartiles.) Step 8: Place a point above the ______Step 9: Place a point above the ______Step 10: Draw the ______

Example 1: 15 shoppers rated a brand of paper towel on a scale 6. Outlier – a number that is much ______than or much from 0-10 ______than the rest of the numbers in a data set 2, 6, 6, 6, 7, 8, 8, 8, 9, 10, 10 Example 1: Below are the weekly earnings for eight Kroger Employees. Find all measures of variation:

$260, $175, $215, $350, $320, $235, $240, $280 Example 2: The box-and-whisker plot below shows the weights, Lesson 5: Sample and Population in pounds, of the dogs that were weighed this morning at a veterinarian’s office. Approximately what percent of the dogs Vocabulary: weighed less than 25 pounds? 1. A sample is a ______selected group that is ______of the population. 2. If the sample is ______of the population, then the measures of central tendency and of variation for the ______and the 1.The box-and-whisker plot shows that the lower quartile of the ______should be similar. data is ______pounds. 3. The larger the ______size, the more accurate the ______. 2.The lower quartile is the median of the lower ______of the data set. 3.The quartiles divide the data into ______. Example 1: Owen took a random sample of 10 students who take 4.What fraction of the data is less than the lower quartile? ______piano lessons at a music school and recorded their ages. The 5.What percent is equivalent to that fraction? director of the school took a census of all 30 students who take piano lessons at the school and recorded their ages. Owen’s Approximately _____% of the dogs weighed less sample data and the director’s census data are show below: than 25 pounds. Owen’s Sample Data: 5, 12, 12, 12, 12, 13, 13, 17, 17, 25 Example 3: The double box-and-whisker plot below shows the number of points scored in games by two basketball players on the same team. Find the range and interquartile range for each player. Director’s Census Data: 5, 7, 8, 9, 10, 10, 11, 11, 11, 11, 12, 12, Who was the most consistent scorer? 12, 12, 12, 13, 13, 13, 13, 14, 15, 16, 17, 17, 17, 18, 19, 21, 21, 25, 30

Find and compare the mean, median, mode, and range of the sample and the census. Example 2: Which of the two samples has measures that are closer to those of the actual population? Lesson 6: Categorical data, numerical data, line plot, pictograph

Vocabulary:

1. Categorical data – data that is a ______or ______2. Numerical data – data that is a ______3. Line plot– each data item is shown as a ______above a ______; good for showing numerical data 4. Pictograph – a graph that shows data using ______or ______

Example 1: Jenny keeps statistics during basketball practice. She recorded the number of free throws each player on the team successfully made out of 15 attempts. Her data are listed below.

Example 3: The manager of an online bookstore kept track of the number of books in each box that was shipped for 100 orders. His 10, 14, 15, 12, 12, 9, 8, 14, 12, 5, 13, 10, 10, 12, 11 assistant randomly selected two samples from his data and calculated the mean and median for each:

Sample A: 4, 7, 9, 9, 10, 11, 12, 15, 20, 26

Sample B: 1, 4, 4, 9, 12

Which sample is more likely to have a mean and a median that are good approximations of the actual mean (12.5) and the actual median (11.5) of the population? Calculate the mean and median Create a line plot to display these data. Then identify the mode. of each sample to determine if your guess was correct or not. Example 2: Leslie surveyed a sample of her classmates. She asked them to name the number of different states they have lived in. She displayed the results of her survey in the line plot below. Identify any outliers for the data. Then find the median and the range, with and without the outlier(s). Does removing the outlier(s) change those measures?

Example 2: The number of words that students in a typing class can type in a minute are listed below. First make a frequency table and then a histogram of the data.

Lesson 7: Histogram, bar graph 25, 19, 23, 29, 34, 26, 30, 34, 33, 20, 35, 35, 25, 29, 36, 22, 34, 15

Vocabulary:

1. Bar graph – uses bars to display ______data; The bars have ______between them

2. Histogram – uses ______to show the frequency of data within ______; NO ______

Example 1: The double bar graph shows the number of tickets sold by four theatres yesterday. What was the mean number of tickets sold by these theatres? Question 1: What percent of students can type 30 or more words per minute

Question 2: How many students type 24 or less words per minute? Lesson 7: Line Graphs and Circle Graphs Example 2: Mandy asked a sample of students at her school to name their favorite subject. Her results are shown above. If 12 Vocabulary: students chose social studies as their favorite subject, what is the total number of students surveyed? 1. Line graph – a type of graph that shows change over ______using a ______connecting data points

2. Circle Graph – displays categories of data as ______of a ______

Example 1: As they exited the voting booths, 2,000 people were asked to identify the mayoral candidate for whom they had voted. Of the people surveyed, how many voted for Milton? How many voted for Johnson? How many voted for Dunbar? Lesson 9: Scatter Plots

Vocabulary:

1. Scatter Plot: a graph in which ______of data are plotted. You can use a scatter plot to determine whether a relationship, or ______, exists between ______of data