Bell Ringer Get out your notebook and prepare to take notes on Chapter 9 Convert your height to inches and be prepared to write this value on the whiteboard.

Bell Ringer Get out your notebook and prepare to take notes on Chapter 9 Convert your height to inches and be prepared to write this value on the whiteboard

Using Graphs to Analyze Data

9.1 Finding Mean, Median, and Mode (Page 412) 9.2 Displaying Frequency (Page 418) Essential Questions: How do we find the mean, median, and mode of a set of values? How do we choose which measure of central tendency to use? When are line plots, frequency tables, and histograms useful?

9.1 Mean, Median, Mode Central Tendency: Single value that summarizes how a set of data is centered 1. Mean: Average Sum of data values divided by the number of data values 2. Median: Middle value when the data values are arranged in numerical order Mean of two middle terms for an even number of data values 3. Mode: Item with the greatest frequency Possible to have no mode, one mode, or more than one mode

9.1 cont. Range: Measure of how spread out the data in a set are Difference between the greatest and least values in a set Outliers: A data item that is much higher or lower than the other data items Have very little effect on the median and mode

9.1 cont. When to use mean, median, and mode: Example: The income of people who live in a town

9.2 Displaying Frequency Frequency Number of times a data item occurs Line Plot Displays data with X marks above each data value on a number line

9.2 cont. Frequency Table Lists frequency of each item in a set of data Histogram Special type of bar graph with no spaces between bars Height of bar shows the frequency Intervals are of equal size and do not overlap

9.1/9.2 - Closure How do we find the mean, median, and mode of a set of values? Mean: the sum of data values divided by the number of data items Median: the middle value or mean of the two middle values Mode: the data value or values that occur most often How do we choose which measure of central tendency to use? Mode: when data is not numerical Mean: when there are no outliers Median: when outliers are likely When are line plots, frequency tables, and histograms useful? Quickly organize and display data Useful when there are a large number of data values

9.1/9.2 - Homework Page 414-416, 2-24 even Page 420-421, 2-22 even

Bell Ringer Get out your 9.1/9.2 homework assignment Get out your notebook and prepare to take notes on Section 9.4 Think of some ways that a graph could be misleading and list them in your notebook

9.4 Reading Graphs Critically (Page 428) Essential Questions: How do we recognize misleading graphs? How do we choose the appropriate scale for a graph?

9.4 cont. Misleading Graphs: A scale that does not begin at zero may be misleading Appropriate Graph Techniques: Scale must include least and greatest values Scale must be divided into equal increments

9.4 cont. Example 1: Explain why the new graph is more clear than the previous graph.

9.4 cont. Note:

9.4 cont. Example 2:

9.4 cont. Example 3: The following graph makes it appear that almost twice as much is earned on Thursday as on Monday. Explain.

9.4 cont. Example 4: Using two different scales, make two bar graphs for the following data. Use a break symbol in only one of the graphs.

9.4 cont. Example 5: 1.The graph makes it appear that about 6 times as many people prefer apple juice to prune juice. Why? The Vertical Scale has a break in it and it begins at 10. 2.How would you redraw the graph to more accurately portray the data?

9.4 - Closure How do we recognize misleading graphs? Not starting at zero on the vertical scale Using intervals that are too small, too large, or unequal How do we choose the appropriate scale for a graph? Use equal intervals Include entire range No breaks in the actual data!

9.4 - Homework Page 429-431, 1-7, 11-16

Bell Ringer Get out your 9.4 homework assignment Get out your notebook and prepare to take notes on Section 9.5 Order the following data values from least to greatest in your notebooks

9.5 Stem-and-Leaf Plots (Page 433) Essential Question: How do we read a stem-and-leaf plot?

9.5 cont. Stem-and-Leaf Plots: Graph that shows numerical data arranged in order Each data item is broken down into a stem and a leaf Stem is on the left and the leaf is on the right

9.5 cont. Example 1: Make a stem-and-leaf plot for the following data:

9.5 cont. Back-to-Back Stem-and-Leaf Plots: Compare two data sets in one stem-and-leaf plot

9.5 cont. Example 4: Make a back-to-back stem-and-leaf plot for the following data:

9.5 - Closure How do we read a stem-and-leaf plot? Use the key to understand the relationship between stem and leaf

9.5 - Homework Page 435-436, 1-9, 12

Bell Ringer Get out your 9.5 homework assignment Get out your notebook and prepare to take notes on Section 9.6 Recall the definition of median

9.6 Box-and-Whisker Plots (Page 438) Essential Question: How do we make a box-and-whisker plot?

9.6 cont. Box-and-Whisker Plot: Graph that summarizes a data set along a number line Quartiles: Divide data into four equally-sized groups 1. Lower Quartile median of the lower half of the data 2. Middle Quartile median of the entire data set 3. Upper Quartile median of the upper half of the data

9.6 cont. Example 1: Write a statement that compares the data in the following box- and-whisker plots:

9.6 cont. Example 2: Write a statement that compares the data in the following box- and-whisker plots: The range for the girls heights is greater than the boys. Overall, the boys tend to be taller than the girls. The girls upper quartile is equal to the boys lower quartile.

9.6 cont. Example 3: Make a box-and-whisker plot for the following data:

9.6 cont. Example 3 (cont.):

9.6 cont. Example 4: Make a box-and-whisker plot for the following data:

9.6 - Closure How do we make a box-and-whisker plot? 1. Order data 2. Find quartiles 3. Draw the box and the whiskers

9.6 - Homework Page 440-441, 2-14 even, 17

Bell Ringer 1. Get out your 9.6 homework assignment 2. Get out your notebook and prepare to take notes on Section 9.7 3. Plot the following points on the coordinate plane:

9.7 Making Predictions From Scatter Plots (Page 444) Essential Question: How can we make scatter plots and use them to find a trend?

9.7 cont. Scatter Plots: Graph that displays two sets of data as ordered pairs Shows whether or not two sets of data are related

9.7 cont. Example 1: Make a scatter plot for the data in the table below: Age (in years) Value (in thousands)

9.7 cont. Example 2: Make a scatter plot for the data below:

9.7 cont. Trends:

9.7 cont. Trend Line: Drawn onto the scatter plot Approximates relationship between data sets Used to make predictions about data values that dont appear on scatter plot Possible to have no trend line

Example 3: Use the following scatter plot to predict the height of a tree that has a circumference of 175 in: 88 ft

9.7 - Closure How can we make scatter plots and use them to find a trend? 1. Plot ordered pairs 2. Draw a trend line 3. Decide whether trend is positive, negative, or no trend 4. Predict values

9.7 - Homework Page 446-447; 1-15

Bell Ringer 1. Get out your 9.7 homework assignment 2. Get out your notebook and prepare to take notes on Section 9.8 3. Pick your favorite type of pizza and put a tally mark in the appropriate box in the following table: Pepperoni Plain Meat Lovers Taco Buffalo Chicken

9.8 Circle Graphs (Page 450) Essential Question: How does a circle graph represent data?

9.8 cont. Circle Graph: Shows how parts of a data set relate to the whole Entire circle = the whole Each sector represents part of the whole Total must equal 100%

9.8 cont. Interactive Circle Graph

9.8 cont. Example 1: 21.3 million people in the US use food pantries each year. How many people who use food pantries is 17 or younger? How many people who use food pantries are 50 or older?

9.8 cont. Example 2: Make a circle graph for the following data:

9.8 - Closure How does a circle graph represent data? Represents a whole Each sector is part of the whole

9.8 - Homework Page 452-453; 2-9, 11-15

Bell Ringer 1. Get out your 9.8 homework assignment 2. Get out your notebook and prepare to take notes on Section 9.9 3. Which type of graph would you use to display the heights of every person in this building?

9.9 Choosing an Appropriate Graph (Page 456) Essential Question: What factors go into our decision about what kind of graph is appropriate for a given set of data?

9.9 cont. Types of Graphs: 1. Line Graph Shows change over time 2. Circle Graph Shows parts of a whole, add to 100% 3. Histogram Divided into intervals, describes frequency 4. Box-and-Whisker Plot Summarizes large amounts of data 5. Stem-and-Leaf Plot Data values are close together, exact values are important 6. Scatter Plot Shows a relationship between two sets of data, ordered pairs

9.9 cont. Examples: Choose the appropriate graph to display the following sets of data: 1. Life span of different animals: bar graph or scatter plot?? 2. Average household income and number of cars: histogram or scatter plot?? 3. Price of a gallon of gas over 12 months: line graph or circle graph?? 4. Students favorite type of music?? 5. Daily high temperatures for the month of May?? 6. Hours of television watched versus hours of working on homework??

9.9 cont. Example 2: Choose the appropriate graph for the following set of data: Intervals AND Frequency

9.9 cont. Example 3: Choose the appropriate graph for the following set of data: Circle Graph

9.9 - Closure What factors go into our decision about what kind of graph is appropriate for a given set of data? Amount of data Time relationships Parts of a whole Occur in intervals

9.9 - Homework Page 457-459; 4-19 (DO NOT GRAPH) Page 462-463; 1-14, SKIP 3, 8

Bell Ringer Get out your notebook and prepare to take notes on Chapter 9 Convert your height to inches and be prepared to write this value on the whiteboard.

Documents

data slide

mode slide

notebook slide

large number of data

town slide

whiteboard slide

middle values mode

number line slide