Transcript Statistics Practice

Statistics Practice
AP Psychology Homework
Answers will be provided in lecture
John runs an experiment in which he is recording how long (in
seconds) it takes each male and female participant to sort
shapes into a Venn diagram.
His hypothesis is that girls will perform the task faster than
boys.
1.
Compute the mode for the females.
1.
Compute the mode for the males.
2.
If you combined the female and male values to
find a mode for the entire data set, you would
have 3 modes (a trimodal data set.) What would
they be?
John’s data
So what?
4. What do the modes in these sets of data tell us about female and male performance
on this test?
5. Would the mode be more helpful to John if the score repeated nearly every trial?
6. What kind of data sets would you want the mode to be a very frequently occurring
number?
Mean
1.
Compute the mean for the females.
2.
Compute the mean for the males.
3.
Compute the mean for the males and females
combined.
John’s data
So what?
4. What conclusions can be drawn about female vs. male time on the sorting task based
on the means we just computed?
5. Can John conclude that his hypothesis was correct based on the values of the means?
Why/ why not?
Median
1.
Compute the median for the females.
2.
Compute the median for the males.
John’s data
So what?
3. What conclusions can you draw about these data sets by knowing the medians?
4. Do the medians allow you to know which group of the 2 had the fastest or slowest times?
3. Do the medians allow you to determine if your hypothesis that girls will perform the task
faster than boys is correct?
Skews...
Graph A:
test results for class A
(y axis = # of students;
x axis = score on 100
point test)
Graph B:
test results for class B
(y axis = # of students;
x axis = score on 100
point test)
Scores scale of 0 - 100
Imagine graphs A and B show the test
results of students in 2 different classes on
an exam.
1. On which side is the majority of the data in
graph A?
2. On which side of the graph are their
outliers?
3. If the teacher of class A relied on the
“mean” of the test scores to determine
how well her students did compared to the
students of class B, would the teacher be
happy or sad to have positive skew?
Scores scale of 0 - 100
1.On which side is the majority of the data in
graph B?
1.On which side of the graph are their
outliers?
1.How does the teacher of class B feel about
using the mean of the test as an indicator of
how well his students overall did compared
to class A? WHY?
Why “mean” can be deceptive...
Mr. Smith and Mrs. Anderson gave the same final exam for their AP Economics class. Both
teachers have 100 students in their classes. Both teachers reported an average score
(mean) for their classes of 75 out of 100 on the final exam.
From this set of data, which of the following can we conclude?
A. Mr. Smith’s and Mrs. Anderson’s students performed equally well on the final
exam.
B. The majority of the students in both classes scored a C on the final exam
(assuming they grade on a standard grade scale.)
C. None of the above!!
Descriptive Stats Part 3
Measurements of variability:
Range
1. Which of the teachers has the
biggest range?
SO WHAT?
2. Which of the following can we conclude based upon knowing the range?
A. Mr. Smith did a better job of preparing his students for the test
B. Mr. Smith has students that are better test takers
C. Mr. Smith’s students studied more effectively for the test
D. On that particular day, Mr. Smith’s students were able to score better.
E. None of the above.
Descriptive Stats Part 3 continued
Measurements of variability: Standard deviation and z scores...
The mean on Mrs. Hunter’s chemistry test is 75. The standard deviation for her data is 15. Her
data is skewed right.
1. Draw a rough graph of her data. (Hint: I have told you the skew so you should draw
one of the 2 “whales”)
1. What does the “15” tell us about the scores in her set of data?
2. What does the right skew tell us about outliers and the mean?
3. Horace has a z score of +1.0. What was his actual test score?
4. Jillian has a z score of -1.5. What was her actual test score?
Let’s try a normal curve problem...
1.
Andrea just got her ACT results (which are distributed normally) and they
say she scored in the 99.87 percentile for reading.
a) What does that tell her about her score compared to the rest of the
ACT test takers?
b) Approx how many standard deviations is she from the mean?
Reviewing the rules of the normal curve
1.
What percent of data always falls within 1 standard deviation of the
mean on a normal curve?
2.
What percent of data always falls within 2 standard deviations of the
mean on a normal curve?
3.
What kind of skew does a normal curve have?
Using Stats to Dana’s CSAP score
1.
Dana just got back is CSAP scores which were normally distributed. His z
score for math was -3.0. His raw score was 316. His brother had a z score
of +3.0 and a raw score of 516.
a)
What was the mean for the CSAP math test?
a)
What was the standard deviation?