Name _______________________________________________
Period __________
Date __________
Analyzing CSAP Data
Data KEY QUESTIONS:
a) In which areas are GSHS students doing well?
b) In which areas are GSHS students doing poorly?
c) Is there any correlation between scores in different areas?
d) Are there any outside influences that could be affecting the scores?
e) Do you think the scores reflect the true ability of the GSHS population?
GROUP ASSIGNMENT: subject = _________________________
grade = ________________________
Organization: Before we start analyzing any of this data it would be really nice to organize it. Please
start by rewriting your data so that it is in order from least to greatest (this will help you when you are
doing any form of data analysis):
Stem-and-Leaf Plots A stem-and-leaf plot is a display that lets you see how data is distributed. Each data value is divided into
stems: ____________________________________ and leaves: ____________________________________.
* Your stems must go in ________________________ and you may NOT skip any numbers.
* You are going to want to order the leaves from _______________________________________________.
Here is an EXAMPLE of what a stem-and-leaf plot looks like
Stems
Leaves
9 4 6 7
These data values are 94, 96, and 97. The leaves are in order
from least to greatest.
10 0 8
11 2 2 3
These data values are 112, 112, and 113.
Key: 11 | 2 = 112
1. Look at your data points. You want to be able to break your data up into meaningful bits. Decide
whether you want to have your stems go up by 10s or by 100s. Please explain why.
2. Make a stem and leaf plot of your data.
Name _______________________________________________ Period __________ Date __________
Stems
Leaves (__________________________________)
3. We are going to make another stem-and-leaf plot but this time we are going to have our stems be
Unsatisfactory (U), Partially Proficient (PP), Proficient (P), and Advanced (A). Use the sheet titled CSAP
cut points to help you figure out what your range should be and then help you place numbers in your
stem and leaf plot.
Stems
Leaves (__________________________________)
U
Range:
PP
Range:
P
Range:
A
Range:
4. What kind of information can you derive from each of the stem-and-leaf plots?
#2 –
#3 –
5. Assess which stem-and-leaf plot tells you more about student performance on the CSAP. Please justify
your answer.
Name _______________________________________________ Period __________ Date __________
COMPARRISON DATA: subject = _________________________ grade = ________________________
Organization: Please organize this data so that it is in order from least to greatest.
Double Stem-and-Leaf Plots
Double stem-and-leaf plots are very valuable for comparing two sets of data. It is really important when
you do this that your stems are the same. Because the ranges of data for different subject matters and
grade levels are so different a double stem-and-leaf plot based on pure numbers would not make any
sense. Because of this, we are going to create a double stem-and-leaf plot based on proficiency.
1. Use the stem and leaf plot from above, and the cut scores for your comparison data, to help you
create a double stem and leaf plot
Leaves (_____________________________)
Stems
Leaves (___________________________)
U
PP
P
A
2. What are the similarities between your original data and your comparison data? What do you
hypothesize is the cause of these similarities?
3. What are the differences between your original data and your comparison data? What do you
hypothesize is the cause of these differences?
Name _______________________________________________
Mean, Median, Mode:
Period __________
Date __________
Mean = ____________________________________________________________________________
to find it you __________________________________________________________________
______________________________________________________________________________
Median = ___________________________________________________________________________
to find it you __________________________________________________________________
______________________________________________________________________________
Mode = ____________________________________________________________________________
to find it you __________________________________________________________________
______________________________________________________________________________
1. Use the scores for your assigned group to find the …
Mean = _______________
Median = _______________
Mode = _______________
2. How do these measures of central tendency compare to each other?
3. Which measure of central tendency do you think best describes your groups data? Please justify your
answer.
4. Use the comparison data to find the …
Mean = _______________
Median = _______________
Mode = _______________
5. What conclusion can you draw from comparing the measures of central tendency from your assigned
group and your comparison group?
6. Can you make any conclusions based on the performance of students? Why or why not?
Name _______________________________________________ Period __________ Date __________
Frequency Tables / Histograms
A frequency table (or histogram) is a bar graph that shows how often a certain event occurs.
To construct a frequency table:
- Determine what values or categories you want to use along your x-axis.
- Determine what category occurs the most, use this number to help you determine your scale.
- Use graph paper or a ruler to make sure your bars are straight and easy to read.
1. Create a frequency table looking at the frequency of proficiency levels based on your original
assigned data. Please just draw your bars (do not color anything in yet).
2. The median is located in which proficiency level? Explain how you know this.
3. Break up your frequency table by finding the number of students who are in the Low third, Middle
third, and High third and plotting these values on top of each other. You will need to look at the Cut
Points and your original data to determine how many students are in each category. Once you do please
determine a color you will use for each of them and create a key for your frequency table.. An example
of the end product is shown below:
Name _______________________________________________ Period __________ Date __________
4. The median is located in which third of which proficiency level? Explain how you know this.
5. Although double stem-and-leaf plots provide a decent comparison, double histograms provide a more
visual comparison. The only difference between a double histogram and a regular histogram is that you
will have two bars directly next to each other in the different groupings. Create a double histogram
comparing your original data and the comparison data looking at frequency of proficiency levels. It will
help to look at your double stem-and-leaf plot
6. What conclusions can you make more clearly from the double histogram compared to the double
stem-and-leaf plot?
7. Where to GSHS students seem to be doing better? Please justify your answer.
8. Does there seem to be any correlation between your assigned data and the comparison data? Please
justify your answer.
Name _______________________________________________
Box and Whisker Plots:
Period __________
Date __________
Quartiles are __________________ that splits your data into ____________________________________.
A quarter is __________ of your data.
To find your Quartiles:
1. Find the ____________________ of the data. This is your _______________________________.
2. Find the _____________________ of the first half of data. This is your _____________________.
3. Find the _____________________ of the second half of data. This is your _________________.
To Construct a Box-and-Whisker plot you…
- Draw a number line that will encompass all your data
- Label the endpoints of your data (minimum and maximum) above the number line
- Label the quartiles above the number line
- Draw your box and whiskers
Here is an EXAMPLE of what a box-and-whisker plot looks like
1. Why is the median the same as the second quartile?
2. Fill in the five number summary for you data:
Minimum = ________
Q1 = ________
Q2 = ________
Q3 = ________
Maximum = ________
3. Decide on a scale for your number line. Remember you need to include all your data, you want to be
able to see your five number summary clearly, and you do not need to include values that do not
include your data (i.e. 0)
4. Construct your box-and-whisker plot.
Name _______________________________________________ Period __________
5. Summarize what the box-and-whisker plot says about your data.
Date __________
Circle Graphs
Circle graphs are created to show parts out of a whole and are thus created using percents.
To create a circle graph…
- Determine what your “whole is”
- Determine what parts you are going to use
- Determine the percent that each part is out of your whole
- Convert the percents into degrees by setting up a proportion. The “whole” or total degrees of a
circle is 360°
- Draw a wedge for each part that is the correct angle. Start by drawing 1 and then draw the next
one so that it starts where the first one ends.
1. Create a circle graph for your original data where
your parts are the four different proficiency levels.
a. To help you create your circle graph fill in the
following table
Number
Percent
Degree
U
PP
P
A
2. Create a circle graph for your comparison data where
your parts are the four different proficiency levels.