Rowen conducts a survey to record the number of movies bought by each customer during a weeklong sale at his store Number of Movies , X Frequency 1 25 2 40 3 35 4 45 20 6 15 Rowen calculates the relative frequencies and rounds to the nearest whole percent. Which of the following is the correct cumulative relative frequency graph for Rowen's data?
Unfortunately, as an AI language model, I cannot display images or graphs. However, I can describe how to approach creating a cumulative relative frequency graph from the given data:
1. Calculate the total number of customers (n) who made purchases during the sale. This is the sum of the frequencies: 25 + 40 + 35 + 45 + 20 + 6 + 15 = 186.
2. Calculate the relative frequency (f) for each value of X by dividing the frequency by n and multiplying by 100 to get a percentage. Round to the nearest whole percent. For example, the relative frequency for X = 1 is (25/186) x 100 = 13%.
3. Calculate the cumulative relative frequency (CF) for each value of X by adding up the relative frequencies for X and all previous values. For example, the CF for X = 3 is the sum of the relative frequencies for X = 1, X = 2, and X = 3: 13% + 22% + 19% = 54%.
4. Plot the cumulative relative frequencies as points on a graph, with the values of X on the x-axis and the CF on the y-axis. Connect the points with a line to create the graph.
Hope this helps!
To find the cumulative relative frequencies, we need to calculate the cumulative frequency first. The cumulative frequency is the running total of the frequencies.
| Number of Movies (X) | Frequency | Cumulative Frequency |
|----------------------|-----------|---------------------|
| 1 | 25 | 25 |
| 2 | 40 | 65 |
| 3 | 35 | 100 |
| 4 | 45 | 145 |
| 5 | 20 | 165 |
| 6 | 15 | 180 |
Now, to find the relative frequencies, we divide each frequency by the total number of movies recorded, which is 180.
| Number of Movies (X) | Frequency | Relative Frequency |
|----------------------|-----------|--------------------|
| 1 | 25 | 25/180 ≈ 0.139 |
| 2 | 40 | 40/180 ≈ 0.222 |
| 3 | 35 | 35/180 ≈ 0.194 |
| 4 | 45 | 45/180 = 0.250 |
| 5 | 20 | 20/180 ≈ 0.111 |
| 6 | 15 | 15/180 ≈ 0.083 |
To find the cumulative relative frequencies, we add up the relative frequencies starting from the lowest values.
| Number of Movies (X) | Cumulative Frequency | Cumulative Relative Frequency |
|----------------------|---------------------|-------------------------------|
| 1 | 25 | 0.139 × 25 ≈ 3.475 |
| 2 | 65 | (0.139 + 0.222) × 25 ≈ 9.025 |
| 3 | 100 | (0.139 + 0.222 + 0.194) × 25 ≈ 15.375 |
| 4 | 145 | (0.139 + 0.222 + 0.194 + 0.250) × 25 ≈ 21.875 |
| 5 | 165 | (0.139 + 0.222 + 0.194 + 0.250 + 0.111) × 25 ≈ 23.275 |
| 6 | 180 | (0.139 + 0.222 + 0.194 + 0.250 + 0.111 + 0.083) × 25 ≈ 24.425 |
Based on this calculated cumulative relative frequency data, we will draw the graph with the number of movies on the x-axis and the cumulative relative frequency on the y-axis.
The graph should start at (1, 3.475) and end at (6, 24.425), and the cumulative relative frequency values should increase gradually as we move from left to right.
Therefore, the correct cumulative relative frequency graph for Rowen's data is the one that shows this trend.