Histograms: Use quantitative Data 1. Create a scale for your x axis 2. Figure out where your data fits into your scale 3. Figure out a scale for your y axis 4. draw in your bars Don’t forget a title/label your axes Like bar graphs but for quantitative data. All bars connected

Step 1. Here is a set of data stating the inches of rain received in the month of March in Tacoma, Washington in 2008 unit is in inches 3, 6, 0, 9, 3.5, 2.7, 6.1, 3.4, 5.6, 2.9, 3.4, 7.8, 0, 0, 0, 7, 2.9, 4.5, 7.9, 3.4, 2.1, 3.2, 3.6, 5.6, 5, 8, 0, 1, 3.6, 9, 0 Data has a small spread (low zero high is 9 so probably want to go by a small number, you should have at least 5 bars I will go by 2’s

Step 2: Place your data 3, 6, 0, 9, 3.5, 2.7, 6.1, 3.4, 5.6, 2.9, 3.4, 7.8, 0, 0, 0, 7, 2.9, 4.5, 7.9, 3.4, 2.1, 3.2, 3.6, 5.6, 5, 8, 0, 1, 3.6, 9, 0 # rangeAmount of numbers that fit into these spots bar bar bar bar bar 5

Step 2: Place your data # rangeAmount of numbers that fit into these spots (bar 1) Bar Bar Bar Bar 53 3, 6, 0, 9, 3.5, 2.7, 6.1, 3.4, 5.6, 2.9, 3.4, 7.8, 0, 0, 0, 7, 2.9, 4.5, 7.9, 3.4, 2.1, 3.2, 3.6, 5.6, 5, 8, 0, 1, 3.6, 9, 0

Step 3: Y axis scale There are only 31 points, so going by a small scale would be better I will go by 2’s The more data points the larger the scale

4. Making the Histogram Inches of rain Rain in March (inches) # of days

Shape Part 1: Mode Shape Part 2: Skew Unimodal, bimodal, and multimodal  Unimodal: one high bar?  Bi Modal: two high bars that are about the same?  Multimodal: three bars that are about the same height Skew right, left, or uniform, centered  Skew Right: tail goes to higher numbers  Skew Left: Tail goes to lower Numbers  Uniform: all bars about the same length 5. Describe The Distribution for all histograms, you must describe shape, center, spread, and whether there are gaps and outliers

Center: Where are the highest bars State where the highest bars are and DON’T FORGET TO INCLUDE YOUR UNITS!!!! List them all

Spread Loose: large range of numbers on x axis Tight: a small range of numbers on x axis

Gaps: Where are there holes? List them all Where are your outliers? List them all Don’t forget your units  Gaps: a hole where there are not any bars.  Example: there is a gap from 2 to 4 ft 5. Describe The Distribution for all histograms, you must describe shape, center, spread, and whether there are gaps and outliers A gap Don’t forget your units Example: there is an outlier from 4-6 feet (for histograms a range) Always isolated(maybe only one or two by each other An outlier

5. What,s the distribution Inches of rain Rain in March (inches) # of days

5. Describing shape center, spread and outliers Shape: unimodal one peak, skew right Center: Center is at 2-4 inches of rain, Spread: Spread tight Gaps and outliers: no gaps and no outliers

For the following data make a histogram and describe the shape, center, spread gaps and outliers Hrs. of sleep over a three week period for Mrs. Chambers 6, 8, 5, 4, 6, 8, 7, 8, 8.5, 9, 5, 7, 8, 7.5, 6, 5, 6.5, 3, 7.5, 8, 8.5 Everyone make their own to get the assignment Don’t forget, at least 5 bars

Do now 10/5 Describe the distribution using complete sentences for the following histogram Hours of time awake # of people Hrs. of time awake for people age 20-35

Quiz on histograms For the following set of data, create a histogram and then describe the distribution # of frogs seen in lake Wapato over a two week period 35, 21, 4, 11, 23, 16, 22, 18, 13, 6, 7, 20, 17, 17,

Stem and Leaf Plots 1. Find the range of your stem (lower numbers on bottom) 2. Organize your data points (leaves) 3. Make your stem and leaf plot 4. Describe the distribution Don’t forget your labels and the title

Step 1. Determine the range of your stem Copy down this data # of pennies found on the ground at Mt. Tahoma in the month of June  5, 0, 9, 6, 8, 12, 15, 0, 9, 7, 11, 13, 32, 6, 6, 4, 2, 7, 9, 5, 6, 7, 0, 1, 9, 13, 16, 7, 9, 4 Find your highest and lowest point If your data has decimals then your stem is the whole numbers If your data had whole numbers then your stem is the tens (0, 10’s, 20’s, 30’s etc)

2. Now place leaves (data points) on the stem Organize your data: Determine if you need to divide your stem (have two sections for each stem because you have a lot of data in one section (For example in this problem we have a lot of single digit #’s Range# of days

3. Create your stem and leaf Plot Create your stem (2 for each number because so much data) Place leaves Make sure data points are from smallest to largest Stem 00 1

3. Create your stem and leaf Plot Don’t forget the Title and make sure you have all 30 points! Stem Pennies found on the ground in June

4. Describe your distribution Don’t forget the Title and make sure you have all 30 points! Stem Pennies found on the ground in June Shape: Skew to higher numbers Or skew to lower numbers Mode: how many peaks Center: Where are all the longest sections Spread: (always tight for stem and leaf or else too much data) Gaps and Outliers List all outliers even if numbers repeat

Individual assignment Make the following 2 stem and leaf plots and describe the distribution. Don’t forget a title and a key for each one Data set 1: # of M&M’s in a two pound bag  223, 184, 265, 255, 254, 265, 275, 289, 253, 265, 248, 265, 235, 265, 278, 256 Data set 2: miles I walked in a two week period  3.2, 1,.5, 3.4, 5, 1, 2, 3.2, 5, 1.2, 2.4, 3.5, 1.8, 2.7

Back To Back stem and Leaf 1. Find high point and low point of data look in both lists 2. Make your stem 3. Plot one set of data on one side of stem and one set of data on the other side of the stem 4. Describe the distributions of both sides separately 5. Don’t forget titles!

1. Find high and low in data Copy down the data and then find your high and low points # of pieces of candy each house gave trick or treating on Alder street: 12, 10, 9, 8, 2, 1, 0, 30, 9, 12 # of pieces of candy I got trick or treating on Lawrence street: 30, 31, 20, 25, 6, 27, 0, 26, 9, 26, 33, 40

2/3: Make stem and plot data Don’t forget Titles and make sure you have all points for both sides! Lawrence Street Candy Alder St. Candy

2/3: Make stem and plot data Don’t forget Titles and make sure you have all points for both sides! Lawrence Street Candy Alder St. Candy

4: Describe Distribution Don’t forget Titles and make sure you have all points for both sides! Lawrence Street Candy Alder St. Candy Alder St. Distribution: Shape: unimodal, skew up Center: 0-9 pieces of candy Spread: Tight Gaps: pieces of candy Outliers: 30 pieces of candy Lawrence St. Distribution: Shape: unimodal, skew up Center: pieces of candy Spread: Tight Gaps: pieces of candy Outliers: 0,6,and 9 pieces of candy

Do now: Make a back to back stem and leaf plot # of fish in Wapato: 10, 20, 30,56, 45, 32, 80, 35, 36, 46, 78 # of fish in lake Tahoma: 23,56, 78, 65, 45, 89, 46, 23, 11, 89, 56, 78, 23, 0, 65

Quiz: stem and leaf plot make them and describe the distributions # of students absent of Fridays in statistics second semester in 2011  3, 0, 5, 2, 3, 4, 2, 3, 6, 7, 15, 0, 1, 3, 4, 5, 7, 9, 3, 3, 2, 7, 1, 0, 0, 5, 8, 9, 15  Now make a back to back stem and leaf plot using the data above and this data then compare their distributions  # of students absent from Algebra on Fridays in 2011  6, 7, 8, 2, 3, 5, 6, 7, 8, 4, 8, 7, 6,9, 12, 13, 5, 6, 4, 3, 4,5,

Dot plots Copy down the data For the following set of data, create a dot plot # of skittles eaten in a day 40, 41, 35, 41, 43, 44, 45, 47, 48, 47, 47, 48, 45, 41, 45, 50, 48, 47, 47, 45, 45, 47, 44, 41, 42, 43, 44, 45

Dot plots # of skittles eaten in a day 40, 41, 35, 41, 43, 44, 42, 47, 48, 47, 47, 48, 45, 46, 45, 50, 48, 47, 47, 45, 40, 47, 44, 46, 42, 43, 44, 45

Dot plots describe distributions Shape skew left, unimodal at 47 skittles (6 times) Tight spread Gap from skittles and 49 skittles Outlier: 35 skittles # of skittles eaten in a day

Dot plot reminders Scale must go by 1 Don’t forget the title Don’t forget to list how many dots are at the mode

Time Plot Copy down the following set of data and notes Year# of A’s in classes Time plots have years on the x axis On y axis is right hand column All dots are connected by a line

Time Plot

You try Make a dot plot and describe distribution  # of A’s on tests: 15, 16, 17, 16, 15, 5, 7, 8, 7, 8, 6, 5, 4, 16, 15, 15, 10, 11, 12, 13, 13, 15, 15 Make a time plot, give max/min and where most data is YrTouchdown’s scored

Things to remember for assignment on time and dot plots 1. your are making a time plot and a dot plot for mean age 2. don’t forget to describe distribution for all dot and time plots 3. don’t forget to do the back of the worksheet 4. don’t forget your units

Dot plot: Make a dot plot and describe the distributions Time plot; make a time plot and give max, min, and most common Ounces of water I drink in a day 50, 49, 58, 45, 52, 52, 51, 58, 56, 57, 62, 58, 59, 50, 58, 57, 58, 56, 56, 52, 51, 58, 58, 52, 50, 51, 49 MonthInches flower grew December.5 January.2 February.3 March.7 April.8 May1.0 June.7 July.6 August.4 Quiz dot and time plot