histograms: use quantitative data 1. create a scale for your x axis 2. figure out where your data...
TRANSCRIPT
Histograms: Use quantitative Data
1. Create a scale for your x axis2. Figure out where your data fits into your
scale3. Figure out a scale for your y axis4. draw in your barsDon’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
# range Amount of numbers that fit into these spots
0-1.999 bar 1
2-3.999 bar 2
4-5.99 bar 3
6- 7.99 bar 4
8-9.99 bar 5
Step 2: Place your data
# range Amount of numbers that fit into these spots
0-1.999 (bar 1) 7
2-3.999 Bar 2 12
4-5.99 Bar 3 4
6- 7.99 Bar 4 5
8-9.99 Bar 5 3
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
2 4 6 8 10 12Inches of rain
14
12
10
8
6
4
2
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 axisTight: 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
2 4 6 8 10 12Inches of rain
14
12
10
8
6
4
2
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
8 10 12 14 16Hours of time awake
654321
# 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 plot4. Describe the distributionDon’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
0-9 23
10-19 6
20-29 0
30-39 1
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
33221100
15-1910-145-90-4
Stem
00
1
3. Create your stem and leaf Plot
Don’t forget the Title and make sure you have all 30 points!
33221100
Stem
2
56123355666677778999990001244
Pennies found on the ground in June
4. Describe your distribution
Don’t forget the Title and make sure you have all 30 points!
33221100
Stem
2
56123355666677778999990001244
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 OutliersList 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 period3.2, 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 stem3. 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!
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001305667
069
Lawrence Street CandyAlder St. Candy
0
220998210
2/3: Make stem and plot data
Don’t forget Titles and make sure you have all points for both sides!
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Lawrence Street CandyAlder St. Candy
4: Describe Distribution
Don’t forget Titles and make sure you have all points for both sides!
43210
001305667
069
Lawrence Street CandyAlder St. Candy
0
220998210
Alder St. Distribution:Shape: unimodal, skew upCenter: 0-9 pieces of candySpread: TightGaps: 20-29 pieces of candyOutliers: 30 pieces of candy
Lawrence St. Distribution:Shape: unimodal, skew upCenter: 20-27 pieces of candySpread: TightGaps: 10-19 pieces of candyOutliers: 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 day40, 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 day40, 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 spreadGap from 26-39 skittles and 49 skittlesOutlier: 35 skittles
# of skittles eaten in a day
Dot plot reminders
Scale must go by 1Don’t forget the titleDon’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
1990 6
1991 4
1992 3
1993 5
1994 5
1995 6
1996 6
1997 2
1998 6
1999 6
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
Yr Touchdown’s scored
1956 2
1957 0
1958 8
1959 7
1960 7
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
Month Inches flower grew
December .5
January .2
February .3
March .7
April .8
May 1.0
June .7
July .6
August .4
Quiz dot and time plot