The following Stem & Leaf plot shows the length distribution (in centimetres) of adult cats.

2

|

0115

3

|

577

4

|

113447

5

|

5678899

6

|

0001128

Determine the following:

The middle 50% of the number of cats is from   to   cats

To determine the middle 50% of the data (which corresponds to the Interquartile Range or IQR), we need to find the first quartile (Q1) and the third quartile (Q3) from the given stem-and-leaf plot. Here's the step-by-step process:

### Step 1: List all the data values in order
The stem-and-leaf plot is:

- 2 | 0115
- 3 | 577
- 4 | 113447
- 5 | 5678899
- 6 | 0001128

Combining all the leaves, we get the following ordered list of lengths in centimeters:
\[ 20, 20, 21, 25, 35, 37, 37, 41, 41, 43, 44, 47, 55, 56, 57, 58, 58, 59, 59, 60, 60, 60, 61, 61, 68 \]

### Step 2: Determine the quartiles
There are 25 data points in the ordered list. The position of Q1 (the first quartile) is given by \(\frac{n+1}{4}\), and the position of Q3 (the third quartile) is given by \(3\left(\frac{n+1}{4}\right)\), where \(n\) is the total number of data points.

For Q1:
\[ \text{Position of Q1} = \frac{25+1}{4} = \frac{26}{4} = 6.5 \]

So, Q1 is the average of the 6th and 7th values:
\[ Q1 = \frac{37 + 37}{2} = 37 \]

For Q3:
\[ \text{Position of Q3} = 3 \left(\frac{25+1}{4}\right) = 3 \left(\frac{26}{4}\right) = 19.5 \]

So, Q3 is the average of the 19th and 20th values:
\[ Q3 = \frac{59 + 60}{2} = 59.5 \]

### Step 3: Determine the middle 50% of the data
The middle 50% of the number of cats is from Q1 to Q3. Hence, the range of the middle 50% is:

From \(37\) cm to \(59.5\) cm.

### Answer:
The middle 50% of the number of cats is from 37 cm to 59.5 cm.

Do you want details or have any questions? Here are five numbered questions you can ask:

1. How do you interpret the leaves in a stem-and-leaf plot?
2. Can you explain the process of finding quartiles in a data set?
3. What is the significance of the middle 50% in a data distribution?
4. How does the stem-and-leaf plot help in understanding data distribution?
5. What is the importance of the interquartile range (IQR) in statistical analysis?

**Tip:** When working with data distributions, visual tools like stem-and-leaf plots and box plots can help you quickly identify key statistical measures such as quartiles and potential outliers.

Learn how to determine the middle 50% of the number of cats based on their length distribution using a stem-and-leaf plot. This problem covers statistical concepts such as the interquartile range (IQR) and involves analyzing data from a visual representation. Suitable for students in Grades 9-12.

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