A survey asked 20 students for their favorite type of music. The results were: Pop, Rock, Jazz, Pop, Classical, Rock, Pop, Jazz, Hip Hop, Pop, Rock, Classical, Pop, Hip Hop, Jazz, Rock, Pop, Classical, Pop, Rock.

(a) Create a frequency distribution table for this data.

Music Type	Frequency
Pop	8
Rock	5
Jazz	3
Classical	3
Hip Hop	2

(b) What percentage of students chose Pop music? $\frac{8}{21} \approx 38.1\%$

Difficult Problems

Misleading Graphs: A company wants to show that its sales have increased significantly. They create a bar graph where the y-axis starts at $90,000 instead of 0.
- (a) Explain why this graph might be misleading. Starting the y-axis at $90,000 exaggerates the visual difference between the bars, making a small increase appear much larger than it actually is. This violates the Area Principle.
- (b) How could the company create a more accurate representation of their sales data? The y-axis should start at 0, or a clear break should be indicated if the axis does not start at 0, to accurately represent the relative magnitudes of the sales figures.
Stem-and-Leaf Plot & Shape: Create a stem-and-leaf plot for the following test scores and describe the shape of the distribution: 78, 85, 92, 70, 65, 88, 95, 72, 81, 60, 90, 75, 83, 68, 79, 87, 80, 74, 91, 84.
- Stem-and-Leaf Plot:
```
6 | 0 5 8
7 | 0 2 4 5 8 9
8 | 0 1 3 4 5 7 8
9 | 0 1 2 5
            
```
- Shape: The distribution appears to be roughly symmetric, possibly slightly skewed to the left due to the longer tail on the lower end, but generally bell-shaped. There are no obvious outliers.

Chapter 3: Numerical Summaries of Data

Easy Problems

Mean, Median, Mode: Find the mean, median, and mode for the following dataset: 10, 12, 15, 12, 18, 13, 12.
- (Sorted: 10, 12, 12, 12, 13, 15, 18)
- Mean: $(10+12+15+12+18+13+12)/7 = 92/7 \approx 13.14$
- Median: 12 (the middle value)
- Mode: 12 (appears most frequently)
Range: What is the range of the dataset: 5, 8, 3, 12, 7, 10? Range = Max - Min = $12 - 3 = 9$.
Z-score Calculation: A data point $x=70$ comes from a distribution with mean $\mu=60$ and standard deviation $\sigma=5$. Calculate its z-score. $z = \frac{x - \mu}{\sigma} = \frac{70 - 60}{5} = \frac{10}{5} = 2$.

Difficult Problems

Mean vs. Median for Skewed Data: A small company has 10 employees. Their annual salaries are: $30,000, $32,000, $35,000, $35,000, $38,000, $40,000, $42,000, $45,000, $50,000, $200,000.
- (a) Calculate the mean and median salary. Mean: Sum $= 547,000$, $n=10$. Mean $= 547,000/10 = \$54,700$. Median: (Sorted: $30k, 32k, 35k, 35k, 38k, 40k, 42k, 45k, 50k, 200k$). Median $= (38,000 + 40,000)/2 = \$39,000$.
- (b) Which measure of center (mean or median) better represents a typical employee's salary? Explain why. The median ($39,000) better represents a typical employee's salary. The mean ($54,700) is highly influenced by the single outlier ($200,000 salary), p