Question

How to calculate mean median and mode?

Answer 1

Calculating the mean, median, and mode of a dataset involves different steps for each measure of central tendency. Here's how you can calculate each one:

### Mean
The mean is the average of a set of numbers. To calculate the mean:

1. **Add all the numbers** together to get a total sum.
2. **Divide the total sum by the number of values** in the dataset.

**Formula:**
\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
\]

**Example:**
For the dataset: 4, 8, 6, 5, 3
Mean = (4 + 8 + 6 + 5 + 3) / 5 = 26 / 5 = 5.2

### Median
The median is the middle value when a dataset is ordered. To find the median:

1. **Sort the dataset** in ascending order.
2. If there is an **odd number of observations**, the median is the middle number.
3. If there is an **even number of observations**, the median is the average of the two middle numbers.

**Example:**
For the dataset: 4, 8, 6, 5, 3
1. Sorted order: 3, 4, 5, 6, 8
2. There are 5 numbers (an odd count), so the median is the third number: 5.

For an even dataset: 3, 4, 5, 6
Median = (4 + 5) / 2 = 4.5

### Mode
The mode is the number that appears most frequently in a dataset. To find the mode:

1. **Count the frequency of each value** in the dataset.
2. Identify the number(s) that appear the most.

**Example:**
For the dataset: 4, 8, 6, 5, 3, 4
The number 4 appears twice, while all others appear once.
So, the mode is 4.

If all numbers appear with the same frequency, the dataset is said to have no mode.

### Summary
- **Mean:** Average of the values.
- **Median:** Middle value when sorted; average of the two middle values if even.
- **Mode:** Most frequently occurring value.

Feel free to ask if you need examples with specific datasets or additional clarifications!