The following frequency distribution presents the numbers of copies sold in 2012 for each of the eight best-selling video games.

Question

Call of duty- 3.5 mil
kinect- 2.9 mil
just dance- 2.5mil
assassin- 2.1mil
madden- 1.9 mil
mario- 1.6mil
mass effect- 1.6mil
NBA- 1.5mil
Construct a relative frequency distribution. Round your answers to three decimal places.

Answer 1

To construct a relative frequency distribution, we first need to determine the total number of copies sold by all eight video games. Then, we can calculate the relative frequency for each game by dividing the number of copies sold by the total.

Here are the sales numbers for each game:

• Call of Duty: 3.5 million
• Kinect: 2.9 million
• Just Dance: 2.5 million
• Assassin's Creed: 2.1 million
• Madden: 1.9 million
• Mario: 1.6 million
• Mass Effect: 1.6 million
• NBA: 1.5 million

Step 1: Calculate the total sales

\[ \text{Total Sales} = 3.5 + 2.9 + 2.5 + 2.1 + 1.9 + 1.6 + 1.6 + 1.5 \]

Calculating this gives:

\[ \text{Total Sales} = 3.5 + 2.9 + 2.5 + 2.1 + 1.9 + 1.6 + 1.6 + 1.5 = 17.6 \text{ million} \]

Step 2: Calculate the relative frequency for each game

Relative frequency is calculated using the formula: \[ \text{Relative Frequency} = \frac{\text{Number of Copies Sold}}{\text{Total Sales}} \]

Now we calculate the relative frequencies:

1. Call of Duty: \[ \text{Relative Frequency} = \frac{3.5}{17.6} \approx 0.199 \]

2. Kinect: \[ \text{Relative Frequency} = \frac{2.9}{17.6} \approx 0.165 \]

3. Just Dance: \[ \text{Relative Frequency} = \frac{2.5}{17.6} \approx 0.142 \]

4. Assassin's Creed: \[ \text{Relative Frequency} = \frac{2.1}{17.6} \approx 0.119 \]

5. Madden: \[ \text{Relative Frequency} = \frac{1.9}{17.6} \approx 0.108 \]

6. Mario: \[ \text{Relative Frequency} = \frac{1.6}{17.6} \approx 0.091 \]

7. Mass Effect: \[ \text{Relative Frequency} = \frac{1.6}{17.6} \approx 0.091 \]

8. NBA: \[ \text{Relative Frequency} = \frac{1.5}{17.6} \approx 0.085 \]

Step 3: Construct the relative frequency distribution table

| Game | Copies Sold (millions) | Relative Frequency | |----------------------|------------------------|--------------------| | Call of Duty | 3.5 | 0.199 | | Kinect | 2.9 | 0.165 | | Just Dance | 2.5 | 0.142 | | Assassin's Creed | 2.1 | 0.119 | | Madden | 1.9 | 0.108 | | Mario | 1.6 | 0.091 | | Mass Effect | 1.6 | 0.091 | | NBA | 1.5 | 0.085 |

Final Note

Ensure that all relative frequencies sum up to approximately 1. In this case:

\[ 0.199 + 0.165 + 0.142 + 0.119 + 0.108 + 0.091 + 0.091 + 0.085 = 1.000 \]

Thus, the relative frequency distribution is constructed accurately.