Data on the shoe sizes of a group of students is shown in the table. Shoe size 34 36 37 38 39 40 41 42 49 Females 10 8. 3

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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## Steps to Create a Box-and-Whisker Plot:

1. **First**, place the five points.
2. **Second**, draw longer vertical lines for the smallest, largest, and median.
3. **Third**, draw a small box that reaches the Lower Quartile (LQ) and Upper Quartile (UQ). The vertical height of the box doesn’t matter.

### Analyze Outliers:

An outlier is:
- A point less than the LQ - 1.5 x IQR (Interquartile Range), or
- Greater than UQ + 1.5 x IQR.

### Diagram Explanation:

- The diagram on the right shows a vertical box-and-whisker plot.
- The box represents the interquartile range (IQR) between the first quartile (Q1) and the third quartile (Q3).
- The line inside the box represents the median.
- The "whiskers" extend to the smallest and largest values that are not outliers.
- Points outside the whiskers are considered outliers and are indicated with dots.
- "Upper fence" and "Lower fence" indicate the thresholds for outliers, calculated as Q3 + 1.5 x IQR and Q1 - 1.5 x IQR, respectively.

### Practice:

**Data on the shoe sizes of a group of students is shown in the table.**

| Shoe size | 34 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 49 |
|-----------|----|----|----|----|----|----|----|----|----|
| Females   | 2  | 2  | 10 | 8  | 7  | 3  | 9  | 1  | 0  |
| Males     | 0  | 3  | 3  | 7  | 12 | 9  | 2  | 0  | 1  | 

**Note:** "MATH IS FUN" is depicted in a decorative design on the page.
Transcribed Image Text:## Steps to Create a Box-and-Whisker Plot: 1. **First**, place the five points. 2. **Second**, draw longer vertical lines for the smallest, largest, and median. 3. **Third**, draw a small box that reaches the Lower Quartile (LQ) and Upper Quartile (UQ). The vertical height of the box doesn’t matter. ### Analyze Outliers: An outlier is: - A point less than the LQ - 1.5 x IQR (Interquartile Range), or - Greater than UQ + 1.5 x IQR. ### Diagram Explanation: - The diagram on the right shows a vertical box-and-whisker plot. - The box represents the interquartile range (IQR) between the first quartile (Q1) and the third quartile (Q3). - The line inside the box represents the median. - The "whiskers" extend to the smallest and largest values that are not outliers. - Points outside the whiskers are considered outliers and are indicated with dots. - "Upper fence" and "Lower fence" indicate the thresholds for outliers, calculated as Q3 + 1.5 x IQR and Q1 - 1.5 x IQR, respectively. ### Practice: **Data on the shoe sizes of a group of students is shown in the table.** | Shoe size | 34 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 49 | |-----------|----|----|----|----|----|----|----|----|----| | Females | 2 | 2 | 10 | 8 | 7 | 3 | 9 | 1 | 0 | | Males | 0 | 3 | 3 | 7 | 12 | 9 | 2 | 0 | 1 | **Note:** "MATH IS FUN" is depicted in a decorative design on the page.
Data on the shoe sizes of a group of students is shown in the table:

| Shoe size | 34 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 49 |
|-----------|----|----|----|----|----|----|----|----|----|
| Females   | 2  | 2  | 10 | 8  | 7  | 3  | 0  | 0  | 0  |
| Males     | 0  | 0  | 3  | 7  | 12 | 9  | 3  | 1  | 1  |

Instructions:
- Draw a box-and-whisker plot for the females and for the males and compare the two plots.
- State whether the box plots are symmetrical.
- Comment on whether there are any outliers.
- Draw the box plots again showing any outliers clearly. Outliers are represented by crosses.
Transcribed Image Text:Data on the shoe sizes of a group of students is shown in the table: | Shoe size | 34 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 49 | |-----------|----|----|----|----|----|----|----|----|----| | Females | 2 | 2 | 10 | 8 | 7 | 3 | 0 | 0 | 0 | | Males | 0 | 0 | 3 | 7 | 12 | 9 | 3 | 1 | 1 | Instructions: - Draw a box-and-whisker plot for the females and for the males and compare the two plots. - State whether the box plots are symmetrical. - Comment on whether there are any outliers. - Draw the box plots again showing any outliers clearly. Outliers are represented by crosses.
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