Review the concepts of mean, median, and mode in statistics.

Mean, Median and Mode: Why do we need them?

1. Mean: The mean, also known as the average, is a measure of central tendency. It is calculated by summing up all the values in a dataset and dividing the sum by the total number of values. The mean is sensitive to outliers, as extreme values can significantly impact its value.
2. Median: The median is another measure of central tendency. It represents the middle value in a sorted dataset. To calculate the median, the data must be arranged in ascending or descending order. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.
3. Mode: The mode is the value that appears most frequently in a dataset. It represents the data point(s) with the highest frequency. A dataset can have multiple modes (multimodal) if multiple values occur with the same highest frequency, or it can have no mode (no value appears more frequently than others).

These measures provide different insights into a dataset’s central tendency:

• Use the mean when you want to represent the average value or when your dataset has a roughly symmetric distribution without significant outliers.
• Use the median when you want to find a robust measure of central tendency that is less influenced by extreme values or when the dataset is skewed or contains outliers.
• Use the mode when you want to identify the most frequently occurring value(s) or when working with categorical or discrete data.

It’s important to choose the appropriate measure based on the characteristics of your data and the specific question or analysis you are addressing.

Let’s go through an example for each of the measures — mean, median, and mode.

Example dataset: [2, 3, 5, 7, 7, 8, 10, 10, 10, 12, 15]

1. Mean: To find the mean, we sum up all the values in the dataset and divide by the total number of values.

Mean = (2 + 3 + 5 + 7 + 7 + 8 + 10 + 10 + 10 + 12 + 15) / 11
Mean = 89 / 11
Mean = 8.09 (rounded to two decimal places)