Math CC7/8 – Mar. 24 Math Notebook: Things Needed Today (TNT): Pencil/Math Notebook/Calculator/ Sample & Population 2.3 Math Notebook: Topic: Histogram & Stem & Leaf Plot HW: Worksheet

What’s Happening Today? Warm up S&P 2.3

Warm Up

Answers

What is a Histogram? Histogram is a bar graph that shows the frequency of data within equal intervals. There is NO space between the bars in a histogram. The horizontal axis of the histogram is separated into equal intervals. The vertical bars represent how many items are in each interval.

How can we tell how many values are in the total data set? What does this histogram tell us? What does a gap between bins mean? How can we tell how many values are in the total data set? It tells us how much money students have in their pockets. The gap between bins mean there is no student with the amount of $4 -$4.99 in their pocket. We can tell how many values are in the total data set by adding the height of each bin.

Bin size does matter..... remember your graph is intended to communicate some sort of coherent information.

1-2 3-4 5-6 7-8 9-10 what should I do first?? 15 5-6 11 Decide on the size of the "bin" ð 7-8 12 9-10 9

Hours of TV Watched Weekly # of students 1-2 3-4 5-6 7-8 9-10 # of hours

What is a Stem-and-Leaf Plot? The stem is the left-hand column and will contain the digits in the largest place. The right-hand column will be the leaf and it will contain the digits in the smallest place.

Lets Make a Stem & Leaf Plot This data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. Then find the number of coaches who coached fewer than 25 years. 33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17 Step 1: Order the data from least to greatest. Since the data values range from 12 to 40, use tens digits for the stems and ones digits for the leaves. 12, 15, 15, 17, 17, 18, 20, 21, 22, 23, 23, 29, 33, 33, 40

Step 2: List the stems from least to greatest on the plot. 12, 15, 15, 17, 17, 18, 20, 21, 22, 23, 23, 29, 33, 33, 40 1 List your stems (tens place #) in order 2 3 4

Step 3: List the leaves for each stem from least to greatest. 1 2, 5, 5, 7, 7, 8 0, 1, 2, 3, 3, 9 3, 3, 2 3 4 12, 15, 15, 17, 17, 18, 20, 21, 22, 23, 23, 29, 33, 33, 40

11 coaches coached fewer than 25 years. Step 4: Add a key and a title. 11 coaches coached fewer than 25 years. # of Years Coached 1 2, 5, 5, 7, 7, 8 0, 1, 2, 3, 3, 9 3, 3, 2 Key: 1 7 means 17 3 4

Title: Soccer Players’ Bounce Your turn: This list shows the number of times each soccer player can bounce the ball on their knee. How many soccer players can bounce the ball more than 36 times? 55, 60, 33, 30, 23, 45, 28, 41, 62, 29, 35, 40, 43, 37, 68, 30, 61, 27, 38, 41 23, 27,28, 29, 30, 30, 33, 35, 37, 38, 40, 41, 41, 43, 45, 55, 60 , 61, 62, 68 Title: Soccer Players’ Bounce 12 soccer players can bounce the ball more than 36 times. Don’t forget a title and key! 2 3 4 5 6 3 7 8 9 0 0 3 5 7 8 0 1 1 3 5 5 0 1 2 8 Key: 2 3 means 23

Stem & Leaf Plots Advantages Disadvantages Can handle extremely large data sets The data is collected in a frequency table Concise representation of data Can be used quickly to organize a large list of data values Convenient to use in determining mean, median & mode of a data set quickly Outliers, or gaps are easily visible Not very informative for a small set of data. Not visually appealing Does not easily indicate measures of centrality for large data sets # must be placed in order of lowest to highest Not good if max or min # lie far away from the rest of your data

Histogram Advantages Disadvantages Works well when the data has a REALLY BIG range There is one set of data Data collected using a frequency table Provides a way to display the frequency of occurrences of data along an interval Use of intervals prevents the calculation of an exact measure of central tendency

Why would you use a stem and leaf plot rather than a histogram? Can you use a histogram for discrete (whole number) values or only for continuous, measured values?

Box-Plots The box plot is a standardized way of displaying the distribution of data based on the minimum, first quartile, median, third quartile, and maximum of the data set.

Box-Plots(continued) A box plot is a good way to summarize large amounts of data. It displays the range and distribution of data along a number line. Box plots provide some indication of the data’s symmetry and skew- ness. Box plots show outliers. Original data is not clearly shown in the box plot; also, mean and mode cannot be identified in a box plot. They can be used only with numerical data.

Remember: Graphs MUST always be clearly labeled. Changing the scales in a graph can make the data look very different, ultimately changing the impression that the graph makes. When comparing two or more sets of data, the scales must be consistent; otherwise, it is difficult to compare the data.

What Graph Would You Choose? The following lists different hypothetical data sets. Which graphical representation would best illustrate the data? Explain. Comparison of the annual snow fall between two snowboarding resorts over several years. The amount of time spent watching TV, in hours, of 200 participants. Wind speed at a windmill farm over a three-week period. Students’ favorite summertime activity.