251x9811 2/11/98
Part I.
ECO251 QBA1
FIRST HOUR EXAM
FEBRUARY 16, 1998
Name __________________
Explain or Define the Following (13 Points Maximum)
a) Field (1)
b) Cell (1)
c) Stubhead (1)
d) I have a table describing the entire adult population of a Southern city. It groups the
population according to age and income. If we define the following categories:
A 'Person is under 30'
B ' Person is 30 or older'
C 'Person has income below $40000
D 'Person has income of $40000 or more'
Are the following classes: (3)
Mutually Exclusive?
Collectively Exhaustive?
A and B
______
_______
B and C
______
_______
A, B and C
______
_______
e) I have a table of the percentage of revenues spent on research and development by a large
number of computer companies. The data distribution is skewed to the right and unimodal. If the
median is 8.05%, where would you expect to find the mean and mode? (Would both be above or
below 8.05% or would they be on either side? If on either side, which is which?) (2)
f) Ogive (1)
g) Ordinal Data (1)
h) Third Decile (1)
i) Platykurtic (1)
j) Explain the difference between a statistic and a parameter (2)
k) I have a table of the percentage of revenues spent on research and development by 50 computer
companies. The least spent by any firm was 5.2% and the most was 13.5%. If this data is to be
presented in six classes, what intervals would you use? - Explain your reasoning using the
appropriate formula. (3)
k) In i) according to Sturges' Rule, How many intervals should you use? (2)
l) I take a sample of 100 from a group of 1000, by rolling a die. I take an alphabetic list of the
names of the individuals, and for each name I roll a die. If the die comes up a 3, I include the
individual in the sample, otherwise I do not. I continue this until I have 100 names. Is this a
Simple Random Sample? Why or why not? (2)
251x9811 2/11/98
Part II. Give Formulas for the Following (12 Points maximum):
a) Population Variance (Definitional formula for grouped data) (2)
b) Geometric Mean
c) Sample Mean (Ungrouped data) (1)
d) Population Standard Deviation (Use words!) (1)
e) Coefficient of Variation ( For a sample)(1)
f) Population Skewness (1)
g) Sample Variance (Ungrouped Data - Computational Formula (2)
h) Kurtosis (Population - Ungrouped) (2)
i) Pearson's Measure of Skewness (2)
j) Compute the Harmonic Mean of the numbers 3, 5 and 7 (2)
k) Explain Chebyschef's Inequality (A formula or diagram may be used) (3)
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Part III. Do the Following Problems (25 Points)
In a period of 10 days you make the following numbers of sales:
Day : 1
2
3
4
5
6
7
8
9 10
Sales: 9
9
9 11 18 12 13 14 15 16
Compute the Following:
a) Mean Sales (1)
b) The Median (1)
c) The Standard Deviation
(3)
d) The 80th Percentile (2)
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2. A sample of bid prices of Bonds last Friday was as follows:
Price
70-79.99
80-89.99
90-99.99
100-109.99
Frequency
4
6
8
22
a. Calculate the Cumulative Frequency (1)
b. Calculate The Mean (1)
c. Calculate the Median (2)
d. Calculate the Mode (1)
e. Calculate the Variance (3)
f. Calculate the Standard Deviation (2)
g. Calculate the Interquartile Range (3)
h. Calculate a Statistic showing Skewness and Interpret it (3)
i. Make a Frequency Polygon of the Data (Neatness Counts!)(2)
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