Title: Warm up
1Warm up
2I use a scale to measure my weight, which I know
is 130. I get on and off several times, and
obtain the following weights 150,
140,130,120,110. Is this valid?
3I use a scale to measure my weight, which I know
is 130. I get on and off several times, and
obtain the following weights 150,
140,130,120,110. Is this biased?
4I use a scale to measure my weight, which I know
is 130. I get on and off several times, and
obtain the following weights 150,
140,130,120,110. Is this reliable?
5Chapter 11Displaying Distributions with Graphs
6Histogram
- The most common graph of the distribution of a
quantitative variable - To create a histogram,
- Divide the range of the data into classes of
equal size. Be sure that each individual fall
into exactly one class. - Count the number of individuals in each class.
- Draw the histogram. Each bar represents a class.
The base of the bar covers the class, and the bar
height is the class count (or percentage).
7Example
- ACT Scores Groups Counts
- 31 26 23 15-18 3
- 32 24 25 19-22 6
- 25 22 30 23-26 7
- 17 18 19 27-30 3
- 15 21 20 31-34 2
- 20 28 24
- 22 29 23
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9Histogram
- Unlike the bars of the bar graph, these bars
should have no space in between them (The only
time there should be a space is if there is no
observations in one of the classes). - There is not one right choice of the class size,
but if you pick too many or too few, it is hard
to tell the shape of the distribution
10Stemplot
- Only use with a small data set.
- To make a stemplot
- separate the numbers into stems and leaves. The
stems can have as many numbers as needed, but the
leaves can only have one number (the final
number). - Write the stems in a vertical column on the left
(starting with the lowest value) and draw a line
to separate them from the leaves. - Write the leaves ascending to the right of the
appropriate stem.
11Stemplot
- If there are equal numbers, then make sure you
account for each one in your plot - Make sure you put equal spacing in between the
numbers. - Once you begin numbering your stems, you cannot
skip a stem
12Example
- 90, 87, 12, 45, 67, 34, 38, 54, 61, 92, 33, 21,
7, 38, 26 - Stem Leaves
- 0 7
- 1 2
- 2 1 6
- 3 3 4 8 8
- 4 5
- 5 4
- 6 1 7
- 7
- 8 7
- 9 0 2
13Stemplot
- If you have a small spread of numbers, you may
want to divide them into smaller groups (ex.
Instead of having all the 30s together, put
30-34 together and 35-39 together) so that you
can see the shape of the distribution more
clearly. - If you have large numbers you may need to round
so that you can limit your number of stems. If
this is done, you need to make sure you label
your graph with the correct information. (ex.
Is your data in hundreds, thousands, millions)
14 Example a small spread of numbers
- 20, 21, 22, 21, 20, 23, 20, 25, 26, 28, 29, 28,
20, 25, 26, 22, 23 - Groups Stem Leaves
- 20-21 2 0 0 0 0 1 1
- 22-23 2 2 2 3 3
- 24-25 2 5 5
- 26-27 2 6 6
- 28-29 2 8 8 9
15Example larger numbers
- 15765 ? 15800 ? stem 15 leaf 8
- 6423 ? 6400 ? stem 6 leaf 4
- 19,333 19,300 ? stem 19 leaf 3
- 842 800 ? stem 0 leaf 8
- You can also use decimals as the leaf. Example
8.6 ? stem 8 leaf 6
16Histogram and Stemplot
- A stemplot looks like a histogram turned on end.
- You can choose the classes in a histogram. The
classes of a stemplot are given to you. - The chief advantage of a stemplot is that it
displays the actual values of the observations.
Stemplot are also faster to draw than histograms. - Stemplots do not work well with large data sets,
because the stems then have too may leaves.
17Interpreting Distributions
- In any graph of data, look for an overall
pattern and for striking deviations from this
pattern - Outlier - individual observations that falls
outside the overall pattern of the graph. - Whether an observation is an outlier is to some
extent a matter of judgment. - Many outliers are due to mistakes. Other outliers
point to the special nature of some observations.
18Is there an outlier in the following graph
19Overall Pattern
- To see the overall pattern, Ignore any outliers.
- See if the Distribution has a simple shape
- Center and Spread
20Shape of a Distribution
- Symmetric right and left sides of the histogram
are approximately mirror images of each other -
21Skewness
- Skewed to the right if the right side of the
histogram extends much farther out than the left
side .(the histogram has a long right tail)
22Skewness
- Skewed to the left if the left side of the
histogram extends much farther out than the right
side (the histogram has a long left tail)
23- Center where the middle of the distribution
seems to be (half of the values are below this
point and half are above) - Spread the lowest and highest numbers obtained
by the graph on the x-axis (usually excluding the
outliers) - We will describe center and spread numerically in
chapter 12.
24Homework
- Ch.111, 2,4,6,7,8,10,12,15,16,17
- To turn in
- 2,4,6,10, 12