what is mean median and mode and range

Mean, median, mode, and range are basic statistics that describe a list of numbers.

Simple definitions

• Mean : The usual “average.”
  Add all the numbers, then divide by how many numbers there are.
  Example: For 2, 4, 6, mean =2+4+63=4=\frac{2+4+6}{3}=4=32+4+6​=4.

• Median : The middle value when the numbers are in order.
  If there are:

  • An odd amount of numbers: it’s the single middle one.
  • An even amount: it’s the average of the two middle numbers.
    Example: For 2, 4, 6, median = 4; for 2, 4, 6, 8, median =4+62=5=\frac{4+6}{2}=5=24+6​=5.

• Mode : The value that appears most often.
  A set can:

  • Have one mode (unimodal)
  • Have more than one mode
  • Have no mode (if nothing repeats)
    Example: In 2, 4, 4, 6, 7, mode = 4.

• Range : How spread out the numbers are.
  Range = largest value − smallest value.
  Example: For 2, 4, 6, 10, range = 10 − 2 = 8.

Quick example with all four

Take the data set: 3, 5, 5, 8, 10.

1. Mean:
   (3+5+5+8+10)÷5=31÷5=6.2(3+5+5+8+10)÷5=31÷5=6.2(3+5+5+8+10)÷5=31÷5=6.2.

2. Median:
   The numbers in order are already: 3, 5, 5, 8, 10 → middle number is 5, so median = 5.

3. Mode:
   5 appears most often, so mode = 5.

4. Range:
   Max = 10, min = 3 → range = 10 − 3 = 7.

Why they matter

• Mean, median, and mode all describe central tendency – where the “center” of the data is.

• Range describes spread – how far apart the values are.

Together they give a quick snapshot of what a data set “looks like.”