Download Alg II Addendum 1 (Stats Ch 15) SAT II Math - Math-SAT-II-Prep

Name:____________________________________
Save this sheet to study for the Math Level II test in June.
Date:
Algebra II Addendum 1 Chapter 15 Math Level II Test Preparation Worksheet
Basic Statistics for the Math Level II test
For the math level II test, you will be expected to enter quantitative data into a list on your TI-83, then create
visual displays and calculate basic statistics that describe the data set.
Entering Data
To enter data into the TI-83, hit STAT then EDIT and type data into one of the lists provided, say L1. Note that
the DEL button is used to delete an individual datum, but use the CLEAR button when the cursor is on L1 to
clear the entire list of data.
Entering Data Organized by Frequencies
When individual data points repeat multiple times, you can put the frequencies into a separate list. Use L2, and
make sure each datum in L1 has the corresponding frequency directly to its right.
For example, the following lists represent the same data set:
List A
List B
data
data
freq
value
0
0
1
1
1
5
1
2
2
1
1
1
2
2
To enter the data in List A format, just enter each datum into L1. To enter it as a frequency table as organized
in List B, use the first three rows of L1 and L2 both.
Descriptive Statistics for Quantitative Data
The mean is the arithmetic average of all the data, a useful measure of the center of the data set. The standard
deviation is a useful measure of the average amount of variation from the mean, telling you how spread out the
data is. Both can be found by selecting STAT then CALC and 1 VAR STATS, followed by the list name (use
the 2nd button and the appropriate number to get the list). If your data is entered as frequencies (see above),
then select 1 VAR STATS L1, L2. Your calculator knows the correct interpretation of the two lists. Mean is
shown with x and standard deviation of a data set is Sx.
Another measure of center is the median, the middle data point. It's less powerful than the mean because it is
less representative of each datum – on the other hand, it can be more reliable than the mean because one outlier,
or extreme point, will not greatly alter the median. The median is the 50th percentile point, or the point at
which 50% of the data is below the median. Similarly, the Interquartile Range, or IQR, gives a measure of
spread that is less sensitive to extreme points, since it is the distance between the 25th percentile (Quartile 1, or
Q1) and the 75th percentile (Quartile 3, or Q3). The 5-number summary consists of the five landmark
percentiles: 0% (the min), 25%, 50% (the median), 75%, and 100% (the max). 1 VAR STATS gives the 5
number summary, from which you can compute the IQR by subtracting Q1 from Q3, and the range, which you
get by subtracting the min from the max.
Name:____________________________________
Save this sheet to study for the Math Level II test in June.
Date:
Visual Displays
A boxplot is a visual display of the 5-number summary, with the
median shown by the line in the middle. The length of the central
box shows the IQR. Putting multiple boxplots next to each other is
an easy way to compare center and spread for multiple data sets. To
make a boxplot, go to 2nd STAT PLOT, turn Plot 1 on, then select the
picture of the boxplot under TYPE. XList has your list, while FREQ
should be 1 unless you are using a frequency list described above, in
which case you put the list of frequencies under FREQ. Make sure
you say ZOOM STAT to get a good picture. The TRACE function
allows you to see the values of the 5-number summary.
A Boxplot.
This boxplot shows an outlier as its min. Note
how small the IQR is compared to the range. In
this case, the IQR isa much more representative
measure of spread for the data set as a whole,
because the range is dominated by the value of a
single point. (The standard deviation is
misleadingly inflated as well.) Likewise, the
median is much safer than the mean as a
measure of center.
A histogram, like a boxplot, is a visual display of quantitative
data. Like a boxplot, it shows the range of the data, but it does
not highlight the 5-number summary. Instead, it gives you a
sense of where all the data lies by grouping it into regular
intervals. It's useful for detecting modes, or values of the
greatest frequency. Likewise, it can also show gaps in the data
A histogram that is unimodal but NOT symmetric, with
outliers. Best summarized with median and IQR.
and other patterns in the data set. Therefore, looking at a
histogram tells you the shape of the data set. If the histogram
is symmetric and unimodal – only one prominent area of greatest frequency at the center of the data set – then
the mean and standard deviation are good ways to summarize the distribution. If the histogram shows multiple
modes, is not symmetric (skewed), or has gaps and outliers, then the mean and standard deviation can be
misleading; the median and IQR are probably safer ways to measure center and spread.
To construct a histogram, follow the instructions above for creating a boxplot but select the little picture of the
histogram under TYPE. Don't forget to ZOOM STAT.
1. In T. Tom's class, 4 students earned 100% on a
quiz, 13 students earned 90%, 3 students earned
80%, and 1 earned 70%. What was the mean
grade?
3. In T. Tom's class, 4 students earned 100% on a
quiz, 13 students earned 90%, 3 students earned
80%, and 1 earned 70%. What was the standard
deviation of the grades?
A. 7.4%
A. 7.4%
B. 89.5%
B. 89.5%
C. 90%
C. 90%
D. 91%
D. 91%
E. 0%
E. 0%
2. In T. Tom's class, 4 students earned 100% on a
quiz, 13 students earned 90%, 3 students earned
80%, and 1 earned 70%. What was the median
grade?
4. In T. Tom's class, 4 students earned 100% on a
quiz, 13 students earned 90%, 3 students earned
80%, and 1 earned 70%. What was the IQR of
the grades?
A. 7.4%
A. 7.4%
B. 89.5%
B. 89.5%
C. 90%
C. 90%
D. 91%
D. 91%
E. 0%
E. 0%
Name:____________________________________
Save this sheet to study for the Math Level II test in June.
5. When T. Sally's class took a quiz, they received
the following scores:
88 84 76 88 84 71 85 62 86 84 80 70 79
75 71 68 91 67 83 81 73 87 85 75 79 95
89 72 63 90 57 74 83 67 81 85 82 78 92
Which of the following is a 5 number summary
of these scores?
A. 57 – 72 – 81 – 85 – 95
B. 57 – 74 – 81 – 86 – 95
C. 57 – 74 – 79 – 86 – 95
D. 57 – 72 – 79 – 85 – 95
E. 57 – 74 – 79 – 86 – 91
6. Which of the following is the best description of
the shape of the distribution of T. Sally's
students' quiz scores given above?
A. unimodal and symmetric
B. unimodal and skewed
C. bimodal and symmetric
D. bimodal and skewed
E. unimodal and symmetric with outliers
7. Which of the below boxplots could represent the
data set of T. Sally's students' scores given
above?
A.
B.
C.
D.
E.
Date: