In the above example, the minimum height value is 85 cm and the maximum height value is 115 cm. What is the range?

Question

Accepted Answer

> [!TLDR]
> The **range** of a dataset is the difference between the maximum and minimum values; it measures the spread of the data in the same units as the original observations.

## Why Range?

Range is the simplest measure of dispersion. While the mean tells you the central tendency, the range tells you how *spread out* your data is. A small range means the values cluster tightly; a large range means they are scattered.

The formula is straightforward:

$$
	ext{Range} = 	ext{Maximum value} - 	ext{Minimum value}
$$

In the height example given, the tallest measurement is $115 \, 	ext{cm}$ and the shortest is $85 \, 	ext{cm}$, so the range is $115 - 85 = 30 \, 	ext{cm}$. This tells you that the heights vary by $30 \, 	ext{cm}$ across the group.

## Computing Range in Python (Pandas)

Suppose you have a DataFrame with a column of heights:

```python
import pandas as pd

# Sample data
data = {'Height_cm': [85, 90, 95, 100, 105, 110, 115]}
df = pd.DataFrame(data)

# Calculate range
height_range = df['Height_cm'].max() - df['Height_cm'].min()

print(f"Range of heights: {height_range} cm")
```

**Output:**
```
Range of heights: 30 cm
```

The `.max()` and `.min()` methods return the largest and smallest values in the Series, respectively. Subtracting them gives the range.

## Computing Range in Python (NumPy)

If you're working with a NumPy array:

```python
import numpy as np

heights = np.array([85, 90, 95, 100, 105, 110, 115])

height_range = np.ptp(heights)  # peak-to-peak

print(f"Range of heights: {height_range} cm")
```

**Output:**
```
Range of heights: 30 cm
```

The `np.ptp()` function (peak-to-peak) computes the range directly. …

X	f	fX
1	5	5
2	9	18
3	12	36
4	17	68
5	14	70
6	10	60
7	6	42
Total	73	299

Marks (X)	1	2	3	4	5
f	8	10	Y	2	4
fX	8	20	3Y	8	20

Q.In the above example, the minimum height value is 85 cm and the maximum height value is 115 cm. What is the range?

Why Range?

Computing Range in Python (Pandas)

Computing Range in Python (NumPy)

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