Math worksheet on box and whisker plots using Herold the cat's weight data.

Let's solve the problem step by step using the data provided in the image.

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Given Data:

Herald's weight (in pounds) over time:
20, 18, 15, 16, 17, 21, 25, 28, 30, 27, 26, 19, 19, 18

We are to analyze this data and answer several questions about box-and-whisker plots and measures of central tendency.

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Step 1: Order the Data

First, sort the weights from smallest to largest:

15, 16, 17, 18, 18, 19, 19, 20, 21, 25, 26, 27, 28, 30

There are 14 data points.

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Step 2: Find the Five-Number Summary

#### Minimum:
Smallest value = 15

#### Maximum:
Largest value = 30

#### Median (Q2):
Since there are 14 values (even), the median is the average of the 7th and 8th values.

- 7th value = 19
- 8th value = 20
- Median = (19 + 20)/2 = 19.5

#### First Quartile (Q1):
Middle of the lower half (first 7 numbers):
15, 16, 17, 18, 18, 19, 19

Median of these = 18

So, Q1 = 18

#### Third Quartile (Q3):
Middle of the upper half (last 7 numbers):
20, 21, 25, 26, 27, 28, 30

Median of these = 26

So, Q3 = 26

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Five-Number Summary:

- Minimum: 15
- Q1: 18
- Median: 19.5
- Q3: 26
- Maximum: 30

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Answering the Questions:

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#### 2. Create a box-and-whisker plot showing Herald’s weight in pounds.

We'll describe how to draw it:

- Draw a number line from 15 to 30.
- Mark the five-number summary:
- Whiskers from 15 to 30
- Box from 18 to 26
- Line inside the box at 19.5

```
|---------------------|--------|---------|----------------------|
15 18 19.5 26 30
Q1 Median Q3
```

(You would draw a box from 18 to 26, a line at 19.5, and whiskers extending to 15 and 30.)

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#### 3. The heaviest 25% of his weight have been greater than ___ lbs.

This refers to the third quartile (Q3) — the value above which lies the top 25% of the data.

So, 26 lbs.

✔ Answer: 26

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#### 4. The middle 50% of Herald’s weight is between ___ and ___ lbs.

The middle 50% is the interquartile range (IQR), between Q1 and Q3.

So, between 18 and 26.

✔ Answer: 18 and 26

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#### 5. If Herald went back to the vet and weighed 36 pounds (too much! too big!), what would the box and whisker plot look like?

Adding 36 to the data set:

New sorted data: