The manager of a bookstore was analyzing the daily sales by genre to gain insight into customer preferences and stock levels. He discovered the bookstore sold 10 Fantasy novels, 12 Science Fiction novels, 8 Action & Adventure novels, 12 Mystery novels, 8 Horror novels, 4 Romance novels and 4 Graphic novels.
a. Use the given information to complete the following table:
Genre	Frequency	Relative Frequency
Fantasy	
0
0.000
Science Fiction	
0
0.000
Action & Adventure	
0
0.000
Mystery	
0
0.000
Horror	
0
0.000
Romance	
0
0.000
Graphic	
0
0.000
Total	
0
0.000
Round relative frequency to 3 decimal places where necessary
b. How many degrees will the segment representing the Action & Adventure genre have on a pie chart?
0
°
Round to the nearest degree
c. What proportion of the daily sales are from the Science Fiction and Action & Adventure genres?
0.000
Round to 3 decimal places
d. What is the relative frequency for the number of Mystery novels sold?
0.000
Round to 3 decimal places

Let's go through each part of the problem step-by-step.

### Part (a): Complete the Table

1. **Frequency Calculation:**
   To fill in the table, list the frequencies (number of books sold) provided for each genre.

2. **Relative Frequency Calculation:**
   To calculate the relative frequency for each genre, divide the frequency of each genre by the total number of books sold.

**Step 1: Calculate the total number of books sold:**

\[
\text{Total} = 10 + 12 + 8 + 12 + 8 + 4 + 4 = 58
\]

**Step 2: Calculate the relative frequency for each genre:**

\[
\text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total}}
\]

Now, we can fill out the table:

| Genre             | Frequency | Relative Frequency |
|-------------------|-----------|--------------------|
| Fantasy           | 10        | \(\frac{10}{58} \approx 0.172\) |
| Science Fiction   | 12        | \(\frac{12}{58} \approx 0.207\) |
| Action & Adventure| 8         | \(\frac{8}{58} \approx 0.138\)  |
| Mystery           | 12        | \(\frac{12}{58} \approx 0.207\) |
| Horror            | 8         | \(\frac{8}{58} \approx 0.138\)  |
| Romance           | 4         | \(\frac{4}{58} \approx 0.069\)  |
| Graphic           | 4         | \(\frac{4}{58} \approx 0.069\)  |
| **Total**         | 58        | **1.000**               |

### Part (b): Degrees for Action & Adventure on Pie Chart

To find the degrees for the Action & Adventure genre in a pie chart, multiply its relative frequency by 360°.

\[
\text{Degrees} = 0.138 \times 360 \approx 50\text{°}
\]

So, the segment for Action & Adventure will have approximately 50°.

### Part (c): Proportion of Sales from Science Fiction and Action & Adventure

To find the combined proportion, add the relative frequencies of Science Fiction and Action & Adventure.

\[
\text{Proportion} = 0.207 + 0.138 = 0.345
\]

So, the proportion of daily sales from Science Fiction and Action & Adventure is approximately 0.345.

### Part (d): Relative Frequency of Mystery Novels

The relative frequency of Mystery novels is already calculated as:

\[
\text{Relative Frequency} = 0.207
\]

### Summary of Answers:

1. **Completed Table:**

   | Genre             | Frequency | Relative Frequency |
   |-------------------|-----------|--------------------|
   | Fantasy           | 10        | 0.172              |
   | Science Fiction   | 12        | 0.207              |
   | Action & Adventure| 8         | 0.138              |
   | Mystery           | 12        | 0.207              |
   | Horror            | 8         | 0.138              |
   | Romance           | 4         | 0.069              |
   | Graphic           | 4         | 0.069              |
   | **Total**         | 58        | **1.000**          |

2. **Degrees for Action & Adventure:** 50°
3. **Proportion from Science Fiction and Action & Adventure:** 0.345
4. **Relative Frequency of Mystery novels:** 0.207

Would you like any more details or further explanations? Here are some related questions you might find interesting:

1. How can we visually represent the data using a bar graph?
2. What is the percentage of sales from the Fantasy genre?
3. How would the pie chart look if another genre was added with 5 books sold?
4. How does the relative frequency change if the total sales increased by 20 books?
5. What is the mean number of books sold per genre?

**Tip:** Always double-check the total frequency and relative frequencies to ensure that they sum to 1 (or 100%) for accuracy.

The manager of a bookstore was analyzing the daily sales by genre to gain insight into customer preferences and stock levels. He discovered the bookstore sold 10 Fantasy novels, 12 Science Fiction novels, 8 Action & Adventure novels, 12 Mystery novels, 8 Horror novels, 4 Romance novels and 4 Graphic novels. a. Use the given information to complete the following table: Genre Frequency Relative Frequency Fantasy 0 0.000 Science Fiction 0 0.000 Action & Adventure 0 0.000 Mystery 0 0.000 Horror 0 0.000 Romance 0 0.000 Graphic 0 0.000 Total 0 0.000 Round relative frequency to 3 decimal places where necessary b. How many degrees will the segment representing the Action & Adventure genre have on a pie chart? 0 ° Round to the nearest degree c. What proportion of the daily sales are from the Science Fiction and Action & Adventure genres? 0.000 Round to 3 decimal places d. What is the relative frequency for the number of Mystery novels sold? 0.000 Round to 3 decimal places.

Analyze the daily sales of a bookstore by genre, including Fantasy, Science Fiction, Action & Adventure, and Mystery novels. Learn how to calculate relative frequency, pie chart degrees, and sales proportions with step-by-step solutions. Suitable for Grades 6-8 students.

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