Introduction

The range of a dataset is the difference between the maximum and minimum values in the dataset. The interquartile range (IQR) is the distance between the first quartile (Q1) and the third quartile (Q3). In this lesson, we will explore how to calculate these measures and understand their significance in data analysis.

Calculating Range and IQR

To calculate the range, we simply find the maximum value in the dataset and subtract the minimum value. The formula for range is:

Range = Maximum - Minimum

To calculate the interquartile range, we first need to identify the median of the dataset. The median is the middle value in the dataset when the values are arranged in order. Once we have the median, we can find the first quartile (Q1) by looking for the value that is one quarter of the way from the minimum to the median. Similarly, we can find the third quartile (Q3) by looking for the value that is three quarters of the way from the median to the maximum. The formula for IQR is:

IQR = Q3 - Q1

Example Problems

1. A teacher recorded the scores of her students on a math test. The scores were: 75, 82, 90, 78, 65, 95, 85, 74, 68, 81. Find the range and IQR of this dataset.
2. A company sells two products, A and B. The prices of these products over time are as follows:

Find the range and IQR of the prices of these products.

Conclusion

In this lesson, we learned how to calculate the range and interquartile range of a dataset. We also saw examples of how to apply these measures in real-world scenarios. Understanding the range and IQR can help us understand the spread of data and make informed decisions based on it.