STAT-402
Statistics and Probability
Assignment # (1)
Q# 1.
The following data show the life time in months of car battery
37
41
39
38
39
41
37
42
40
48
45
47
46
50
51
46
48
49
48
50
52
49
51
55
53
57
55
56
57
62
Display the data by using frequency distribution (considering life as a continuous variable) and stem and
leaf plot
1. Construct histogram and discuss shape of the data
2. Construct dot diagram.
3. Find median and three quartiles.
4. Construct cumulative frequency polygon and by using the graph answer the following.
a. Estimate 50% of batteries have life at most how many months
b. Estimate percentage of batteries that have life at most 54 months
c. Estimate percentage of batteries that have life at least 47 months
Q# 2.
Guests staying at Marada Inn were asked to rate the quality of their accommodation as being
excellent, above average, average, below average, or poor.
The ratings provided by a sample of 20 guests are shown below.
Below
Above
Above
Above
Above
Above
Below
Above
Average
Average
Average
Average
Average
Average
Average
Average
Average
Below
Average
Poor
Poor
Above
Excellent
Average
Average
Above
Average
Average
Average
Above
Average
Average
1. Construct frequency distribution of the above data, also calculate percentage frequency.
2. Construct simple bar chart and pie diagram of the above data.
STAT-402
Statistics and Probability
Q# 3.
Three teachers of statistics reported mean examination grades of 75, 82 and 84 for their classes
each consists of 30, 25 and 17 students respectively. Determine the mean grade for all classes.
Q# 4.
If an investor buys 200 shares at a price of Rs.45/- each and 250 shares at Rs36/ each find the
mean price per share. If he sells all the shares at the mean price of Rs 42/-each share find the amount
of total profit
Q# 5.
Jim’s Videotaping Service recently placed an order for VHS videotape. Jim ordered 6 cases of
High-Grade, 4 cases of Performance High-Grade, 8 cases of standard, 3 cases of High Standard, and 1
case of Low Grade. Each Case contains 24 tapes. Suppose a case of High-Grade costs $28, Performance
High-Grade costs $36, Standard costs $16, High Standard costs $18, and Low costs $16
1.
What is the average cost per case to Jim?
2.
What is the average cost per tape to Jim?
3.
Suppose Jim will sell any tape for for $1.25. is this a good business practice for Jim?
Q# 6.
If a student got 56 and 46 in two mid tests and 65 in a final test find mean marks in three tests
if importance of final test is twice than that of each mid test
Q# 7.
A computer calculated a mean value of 42 from 20 observations. It was later discovered at the
time of checking that two values 45 & 38 entered instead of 35 & 58. Find the correct value of mean.
Q# 8.
Find out missing values in the following table.
Classes
10-19
20-29
30-39
40-49
50-59
60-69
TOTAL
Frequency
?
55
?
40
?
?
250
Relative Frequency
.06
?
0.36
?
?
0.02
1.00
Q# 9.
Car rental rates per day for a sample of seven Eastern U.S. cities are as follows (The Wall Street
Journal, January 16, 2004).
City
Boston
Atlanta
Miami
New York
Orlando
Pittsburgh
Washington, D.C.
Daily Rate $
43
35
34
58
30
30
36
STAT-402
Statistics and Probability
1. Compute the mean, variance, and standard deviation for the car rental rates.
2. A similar sample of seven Western U.S. cities showed a sample mean car rental rate of $38 per day.
The variance and standard deviation were 12.3 and 3.5, respectively. Discuss any difference between
the car rental rates in Eastern and Western U.S. cities.
Q# 10.
Public transportation and the automobile are two methods an employee can use to get to work
each day. Samples of times recorded for each method are shown. Times are in minutes.
Public Transportation: 28
29
32
37
33
25
29
32
41
34
Automobile: 29
31
33
32
34
30
31
32
35
33
a.
Compute the sample mean time to get to work for each method.
b.
Compute the sample standard deviation for each method.
c.
On the basis of your results from parts (a) and (b), which method of transportation should be preferred?
Explain.
d.
Develop a box plot for each method. Does a comparison of the box plots support your conclusion in
part (c)?
Q# 11.
The National Association of Realtors reported the median home price in the United States and
the increase in median home price over a five-year period (The Wall Street Journal, January 16, 2006).
Use the sample home prices shown here to answer the following questions. Data are in thousands of
dollars.
995.9
48.8
628.3 111.0
175.0 263.5
298.0
218.9
209.0
212.9
2325.0
958.0
212.5
192.6
a.
What is the sample median home price?
b.
In January 2001, the National Association of Realtors reported a median home price of $139,300 in the
United States. What was the percentage increase in the median home price over the five-year period?
c.
What are the first quartile and the third quartile for the sample data?
d.
Provide a five-number summary of the home prices.
e.
Do the data contain any outliers?
f.
What is the mean home price for the sample? Why does the National Association of Realtors prefer to
use the median home price in its reports?
STAT-402
Q# 12.
Statistics and Probability
The following data shows the weight (in grams, rounded to the nearest gram) of 35 randomly picked
oranges from a farm.
155, 161, 164, 166, 168, 170, 172, 172, 173, 175, 177, 178, 178, 179, 181, 182, 182, 184, 186, 188, 189, 192,
195, 196, 197, 198, 203, 206, 208, 209, 210, 214, 218, 221, 243
a. Group the data in the form of a table with class intervals.
b. Draw cumulative frequency polygon and calculate the values of three quartiles.
c. Draw a histogram from the above grouped data and calculate mode of the data.
d. Suggest whether the data is positively skewed, negatively skewed, or symmetrical.
e. Construct Box and whisker plot and discuss shape of the data.
Q# 13.
The high costs in the California real estate market have caused families who cannot afford to buy bigger homes
to consider backyard sheds as an alternative form of housing expansion. Many are using the backyard structures for
home offices, art studios, and hobby areas as well as for additional storage. The mean price of a customized wooden,
shingled backyard structure is $3100 (Newsweek, September 29, 2003). Assume that the standard deviation is $1200.
a. What is the z-score for a backyard structure costing $2300?
b. What is the z-score for a backyard structure costing $4900?
c. Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier.
d. The Newsweek article described a backyard shed-office combination built in Albany, California, for $13,000.
Should this structure be considered an outlier? Explain.
e. If Z-score of a backyard structure is 1.5, find the cost of backyard structure.
Q# 14.
Ahmad uses motor cycle to commute daily from his home to his university. On average, the trip one way
takes 24 minutes with a standard deviation of 3.8 minutes. Whereas Aslam, living in a village, use local bus to
commute daily from his home to his university . On average, the trip one way takes 2.3 hours with a standard
deviation of 0.3 hours. On one day Ahmad takes 30 minutes and Aslam takes 2.4 hours on the way to the
university, which student takes more time than usual arrival time.
STAT-402
Statistics and Probability
Q# 15.
The following data represent the daily sales in $1000 and percentage of days for corresponding sale, find
mean daily sale.
Daily sales
% days
0
0.20
1
0.30
2
0.25
3
0.15
4
0.10
Q# 16.
Cool Tel is a large mobile service provider. It has conducted a study on 10,000 customers about the
length of time they have to wait, at its customer care centers, before being facilitated by the Cool’s officer. The
results of the study are as follows:
Waiting Time (min)
0
1
2
3
4
5
6
7
No. of customers
380
1120
1680
1780
1960
1550
1200
330
Find mean waiting time.
Q# 17.
The following data represent the measurements made by to instruments local and imported, which
equipment yield more consistent measurements.
Local
Imported
Q# 18.
7.6
7.2
5.6
7.1
6.5
7.0
7.3
7.1
9
7.3
7.6
7.2
7.2
7.1
7.1
7.2
Consider the following Stem and Leaf display of marks obtain by students.
2 25462
3 365487
4 2232121
5 36587444
6 69876
Find the mean, median and mode of the data and discuss its shape.
7.0
7.3
STAT-402
Statistics and Probability
To compare monthly starting salaries for business school graduates by major, a sample of recent
Q# 19.
graduates was selected. The major and the monthly starting salary were recorded for each graduate.
Following Figure shows box plots for accounting, finance, and management majors.
9000
8000
Salary
7000
6000
5000
4000
3000
Accounting
Finance
Degree
a)
Which degree has the highest average starting salary.
b)
Which degree has more variation in starting salary.
c)
The shape of which degree is close to symmetric.
d)
The shape of which degree is extremely positively skewed.
e)
Employee of which degree has least starting salary
f)
Employee of which degree has highest starting salary.
Management