Find the mean, median and mode of 1, 2, 3, 4, 4.

How we read your problem

Measures of central tendency for a list of numbers.

Step-by-step solution

1. 1

   Sort the data from smallest to largest

   $$1, 2, 3, 4, 4\quad (n = 5)$$
2. 2

   Mean: add the values and divide by how many there are

   $$\bar{x} = \frac{14}{5} = 2.8$$
3. 3

   Median: the middle value of the sorted list

   With 5 values (odd), the median is value number 3.

   $$\text{median} = 3$$
4. 4

   Mode: the value(s) that appear most often

   Most frequent: 4.

5. 5

   Range: largest minus smallest

   $$4 - 1 = 3$$

Formulas used

• Mean

  $$\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$$

• Range

  $$\text{range} = x_{\max} - x_{\min}$$

The mean balances all values, the median splits the sorted data in half and is less affected by outliers, and the mode is the most common value.

Verification

• Sum 14 = mean × n = 2.8 × 5 = 14