1. Consider the following data , showing the distance ( in miles) from home to work for

19 residents of St. Paul:

1 1 2 2 2 3 3 3 3 4 4 4 5 5 6 7 8 8 40

a.) If a researcher wants to know the distance driven by the average resident of St. Paul, is

the above data from a population or from a sample? Explain. (3 points, out of

100 total)

b.) Solve for the mode of the data set. (2)

c.) Solve for the mean of the data set ( show a formula, including only numbers, that, if

solved, would provide the mean; you may then solve for the mean using the

statistical functions on a calculator). (3)

d.) Solve for the median of the data set. (2)

e.) Which is greater, the mean or the median? Explain why ( intuitively, with reference to

the data set). (2)

2. Consider the following sample data , on the percentage change in the value of the given company's stock on January 26, 2022 ( note : Intel is the only positive number; every other data point is negative):

Amazon - .80

Best Buy - 1.13

Comcast - 2.44

Disney - 2.13

ExxonMobil - 1.01

Ford - .35

General Electric - 1.96

Hershey - .33

Intel + 1.35

a.) Solve for the median. (2)

b.) Solve for the sample mean. (2)

c.) What type of skew does this data set exhibit? Explain how you can tell ( based on

your answers to a.) and b.)). (3)

3 . Consider a data set, with 75 observations.

For this data set, you know:

Mean = 25.00

Sample Standard Deviation = 11.00

Then two new data points are added to the set : 1 and 49.

Note that, after these two points are added, the mean of the new data set ( with 77

observations ) is still equal to 25.00.

Solve for the population variance of the new data set ( with 77 observations). Show your work ( you may have to round your final answer to the nearest hundredth) . (3)

4. Consider the following data, which details the current average long-term interest rate

( on government debt) for a group of 12 countries :

Australia 1.8 % England 1.2 South Africa 9.4

Brazil 11.3 India 6.6 South Korea 2.4

Canada 1.7 Indonesia 6.3 Turkey 23.0

China 2.6 Mexico 7.8 USA 1.7

a.) Solve for the range of the data. (2)

For now, consider this to be data from a sample.

( Note: for all calculations in # 4 and # 5, you can round all of your work to the nearest hundredth ( i.e., 2 digits after the decimal). As an example, you can round the mean to the nearest hundredth, and then use that rounded mean when you calculate "squared deviations" , and then round those squared deviations to the nearest hundredth, etc.)

b.) Solve for the sample mean. (2)

c.) Solve for the "sum of the squared deviations". (4)

d.) Solve for the sample variance. (3)

e.) Solve for the sample standard deviation. (2)

Now consider the data to be a population of countries.

f.) Solve for the population variance ( do not use the statistical functions on a calculator;

find it by using your answer to c.) and one other number ; show your work). (3)

g.) Solve for the population standard deviation. (2)

h.) Solve for the median of the population data ( i.e, all 12 countries). ( 1)

i.) Solve for all four quartiles of the population data. Show your work. (4)