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Statistics Homework Questions and Solutions

## Question 1: Variable Classification and Level of Measurement

Question 1

Classify the following variables as qualitative, quantitative discrete, or quantitative continuous. In addition, determine the level of measurement (Nominal, Ordinal, Interval, Ratio) for each variable.

( a ) Number of siblings
( b ) Highest education degree obtained
( c ) Student enrolment in Yorkville University over the recent three years
( d ) Length of time of residence in a city
( e ) Political party affiliation
( f ) Speed of an automobile

Question 2

You are asked to select a random sample of ten people from a group of 200 people using systematic sampling. If the first selection in your sample corresponds to the number 13, then what is the number of the person corresponding to the third selection?

Question 3

ABC Carriers employs 120 drivers, 240 staff, and 60 mechanics. A committee of 7 members is to be formed among all the employees of the company. How many of each type of employees (drivers, staff, and mechanics) are to be selected so that there is as close a representation as possible without bias towards any individual or groups?

Question 4

Sixty full-time students were asked the number of courses they were taking this semester. The (incomplete) results are shown below:

No. of courses Frequency
Relative
Frequency
Percent
Frequency
2 3
3 6
4 30
5 12
6 9
( a ) Complete the table.
( b ) Complete the cumulative frequency table below.

( c ) Compute the mean and the standard deviation of the dataset.

Question 5

The following is the record of “the number of nights going out for dinner last month” for a random selection of 23 employees from a company with several hundred employees.

7 2 9 4 15 13 12 15 27 15 12
5 7 9 5 6 10 9 10 14 24 6 3
( a ) Construct a stem-and-leaf plot.
( b ) Compute the mean and the median of the dataset.
( c ) Find the mode of the dataset. Is the dataset unimodal or bimodal (or neither)?
( d ) Compute the interquartile range (IQR). Use the IQR rule to determine whether
there is any outlier.
( e ) Compute the 30th percentile and the 90th percentile.
( f ) Give the five-number summary of the dataset.

Question 6

An insurance company reports the following distribution of the claim sizes for an auto insurance policy from a sample of 87 cases. Claim Size (in \$) Number of claims

2000 to 3000 15
3000 to 4000 10
4000 to 5000 20
5000 to 6000 15
6000 to 7000 10
7000 to 8000 10
8000 to 9000 7

( a ) Construct a histogram for the data.
( b ) Construct a frequency polygon for the data.
( c ) Compute the mean and the standard deviation of the claim size.
( d ) Find the percentage of claims whose claim size is less than \$7000.
( e ) Find the percentage of claims whose claim size is at least \$5000.
( f ) Find the percentage of claims whose claim size is \$8000 or above.