Download ExamI grades

Due 10/8
Name________________
Math 116 – Take Home related to the exam I grades – Fall 2009
In this problem, the population (individuals and variable) are the grades of ALL students taking
statistics with me in the Fall semester of 2009
1) By just looking at the graphs, which class do you think did better? Explain. Which one is your
class? Let’s label the graphs.
2) Here are the summary statistics for the three classes. Why are they statistics and not
parameters?
A
B
C
D
F
mean
Std-deviation
Min
Q1
Med
Q3
max
Sample size
Complete this
8 am
11 am
2 pm
8
9
6
1
2
82.8
12.3
54
78
85.5
92
100
12
7
3
3
2
83.8
14.3
46
78
88
95
98
9
8
6
4
1
82.2
12.8
47
73
83.5
92.5
101
3) The shape of the distribution of grades of the 11 am class is:
Symmetrical, bell
left skewed
right skewed
4) Consider the top graph. The lower whisker is longer than the upper whisker. What is the
meaning of this?
1
5) Use the statistics of Exam 1 to complete the following:
a) For the 8 am class, the middle 50% of the data are between _________ and _________
b) The top 75% of the 11 am class compares to the top 75% of which other class?
c) For the 11 am class, 25% of the students scored at or below ________________
d) For the 2 pm class, 75% of the students scored at or above ________________
e) What is the 25th percentile of the class corresponding to the top graph?
5) If a student is selected at random from the population, what is the probability that the student
selected got an A? Show how you find it. Round answer to 3 decimal places
6) a) Using the standard deviation as a unit - Use the mean and standard deviation of each class (see
page 1) and label the tick marks of the following diagrams. Locate the mean at the X.
8 am class
_|________|________|________|________X________|________|________|________|__
11 am class
_|________|________|________|________X________|________|________|________|__
2 pm class
_|________|________|________|________X________|________|________|________|__
b) Complete the following:
8 am class 11 am class 2 pm class
Unusually low values are lower than
Unusually high values are higher than
2
7) How many standard deviations from the mean is a given score?
There is a number called a z-score that tells you the number of standard deviations that a certain
number is above or below the mean. Here is the formula
yourscore  mean
z
z-score = (score – mean) / standard deviation
s tan dard .deviation
Use the formula to find the z-score corresponding to a score of 70. Round to two decimal places Show work
8) By the range rule of thumb any number which is more than ________ standard deviations away
from the mean is considered an unusual value in the distribution.
REWRITE this rule using z scores:
9) DO THIS AT HOME, ON ANOTHER PAPER – for your info only – I don’t want this back
This will help you compare your grade to the grades of all students in your class.
What is your grade? What is the z-score of your grade? Is your grade usual or unusual? If
unusual, is it unusually low or high?
10) Frequency tables – relative frequency tables – probability distributions
Let’s copy here the grouped data of YOUR CLASS
Classes
??????
Frequency
Relative
frequency
Probability
11) Use the calculator to find the statistics of the grouped data
12) Use the calculator to find the statistics of the probability distribution
3