Chapter 3.1, Problem 12E

Online Multiplayer Game Downloads. The creator of a new online multiplayer survival game has been tracking the monthly downloads of the newest game. The following table shows the monthly downloads (in thousands) for each month of the current and previous year.

1. a. Compute the mean, median, and mode for number of downloads in the previous year.
2. b. Compute the mean, median, and mode for number of downloads in the current year.
3. c. Compute the first and third quartiles for downloads in the previous year.
4. d. Compute the first and third quartiles for downloads in the current year.
5. e. Compare the values calculated in parts a through d for the previous and current years. What does this tell you about the downloads of the game in the current year compared to the previous year?

To determine

Find the mean, median and mode for the number of downloads in previous year.

Answer to Problem 12E

The mean, median and mode for the number of downloads in previous year are 34.1818, 34, and 34, respectively.

Explanation of Solution

Calculation:

The data represent the monthly downloads (in thousands) for 11 months in previous year and monthly downloads (in thousands) for 10 months in current year.

Software Procedure:

Step by step procedure to obtain the descriptive statistics using EXCEL is as follows:

• In an EXCEL sheet enter the observations of first sample and label it as Previous.
• Go to Data > Data Analysis (in case it is not default, take the Analysis ToolPak from Excel Add Ins) > Descriptive statistics.
• Enter Input Range as $A$2:$A$12, select Columns in Grouped By, tick on Summary statistics.
• Click on OK.

Output using EXCEL is given as follows:

From the EXCEL output, mean, median, and mode for the number of downloads in previous year are 34.1818, 34, and 34, respectively.

Thus, the mean, median, and mode for the number of downloads in previous year are 34.1818, 34, and 34, respectively.

To determine

Find the mean, median and mode for the number of downloads in current year.

Answer to Problem 12E

The mean, median and mode for the number of downloads in current year are 35.9, 37, and 37, respectively.

Explanation of Solution

Calculation:

Software Procedure:

Step by step procedure to obtain the descriptive statistics using EXCEL is as follows:

• In an EXCEL sheet enter the observations of second sample and label it as Current.
• Go to Data > Data Analysis (in case it is not default, take the Analysis ToolPak from Excel Add Ins) > Descriptive statistics.
• Enter Input Range as $A$2:$A$11, select Columns in Grouped By, tick on Summary statistics.
• Click on OK.

Output using EXCEL is given as follows:

From the EXCEL output, mean, median and mode for the number of downloads in current year are 35.9, 37, and 37, respectively.

Thus, the mean, median and mode for the number of downloads in current year are 35.9, 37, and 37, respectively.

To determine

Find the first and third quartiles fir downloads in previous year.

Answer to Problem 12E

The first and third quartiles fir downloads in previous year are $\underset{\_}{Q_1=33}$, and $\underset{\_}{Q_3=35}$, respectively.

Explanation of Solution

Calculation:

The first and third quartiles are obtained using EXCEL functions.

First quartile:

The EXCEL function to compute first quartile is $Q_1=\text{QUARTILE}\text{.EXC}\left(\text{input range,1}\right)$.

Software Procedure:

Step by step procedure to obtain the first quartile using EXCEL is as follows:

• In an EXCEL sheet enter the observations of first sample and label it as Previous.
• In a cell enter the formula QUARTILE.EXC ($A$2:$A$12,1).
• Click on OK.

Output using EXCEL is given as follows:

From the EXCEL output, the first quartile is 33.

Third quartile:

The EXCEL function to compute third quartile is $Q_3=\text{QUARTILE}\text{.EXC}\left(\text{input range,3}\right)$.

Software Procedure:

Step by step procedure to obtain the third quartile using EXCEL is as follows:

• In an EXCEL sheet enter the observations of first sample and label it as Previous.
• In a cell enter the formula QUARTILE.EXC ($A$2:$A$12,3).
• Click on OK.

Output using EXCEL is given as follows:

From the EXCEL output, the third quartile is 35.

Thus, the first and third quartiles fir downloads in previous year are $\underset{\_}{Q_1=33}$, and $\underset{\_}{Q_3=35}$, respectively.

To determine

Find the first and third quartiles fir downloads in current year.

Answer to Problem 12E

The first and third quartiles fir downloads in current year are $\underset{\_}{Q_1=34.5}$, and $\underset{\_}{Q_3=37}$, respectively.

Explanation of Solution

Calculation:

The first and third quartiles are obtained using EXCEL functions.

First quartile:

The EXCEL function to compute first quartile is $Q_1=\text{QUARTILE}\text{.EXC}\left(\text{input range,1}\right)$.

Software Procedure:

Step by step procedure to obtain the first quartile using EXCEL is as follows:

• In an EXCEL sheet enter the observations of second sample and label it as Current.
• In a cell enter the formula QUARTILE.EXC ($A$2:$A$11,1).
• Click on OK.

Output using EXCEL is given as follows:

From the EXCEL output, the first quartile is 34.5.

Third quartile:

The EXCEL function to compute third quartile is $Q_3=\text{QUARTILE}\text{.EXC}\left(\text{input range,3}\right)$.

Software Procedure:

Step by step procedure to obtain the third quartile using EXCEL is as follows:

• In an EXCEL sheet enter the observations of second sample and label it as Current.
• In a cell enter the formula QUARTILE.EXC ($A$2:$A$11,3).
• Click on OK.

Output using EXCEL is given as follows:

From the EXCEL output, the third quartile is 37.

Thus, the first and third quartiles for downloads in current year are $\underset{\_}{Q_1=34.5}$, and $\underset{\_}{Q_3=37}$, respectively.

To determine

Compare the values of mean, median, mode, and quartiles for the two samples.

Explanation of Solution

The mean, median, and mode for the number of downloads in previous year are 34.1818, 34, and 34, respectively.

The first and third quartiles for downloads in previous year are $Q_1=33$, and $Q_3=35$, respectively.

The mean, median and mode for the number of downloads in current year are 35.9, 37, and 37, respectively.

The first and third quartiles for downloads in current year are $Q_1=34.5$, and $Q_3=37$, respectively.

Here, all the values of mean, median, mode, first quartile, and third quartile are higher for the sample of current year.

From this it can be said that, the number of downloads are more in current year than in previous year.