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what is the mean median mode and range

Mean, median, mode, and range are four basic ways to describe a set of numbers in statistics. They tell you about the “center” and the “spread” of the data.

Mean (the usual “average”)

  • Add up all the numbers.
  • Divide by how many numbers there are.
  • Example: For 3, 5, 7, the mean is (3+5+7)÷3=15÷3=5(3+5+7)÷3=15÷3=5(3+5+7)÷3=15÷3=5.

The mean is sensitive to very large or very small values (outliers), so one extreme number can pull it up or down a lot.

Median (middle value)

  • Put the numbers in order (smallest to largest).
  • If there are an odd number of values, the median is the one in the middle.
  • If there are an even number of values, the median is the average of the two middle numbers.

Example: For 2, 4, 9, 10, 15, the median is 9 (the middle value in the ordered list).

The median is useful when data has extreme values, because it ignores how big the extremes are and just cares about position.

Mode (most common value)

  • The mode is the value that appears most often in the data set.
  • A data set can have:
    • No mode (no value repeats),
    • One mode (unimodal),
    • Or more than one mode (bimodal, multimodal).

Example: In 2, 4, 4, 5, 7, 7, 7, the mode is 7, because it appears the most times.

The mode is especially handy for categorical data like “red, red, blue, green” where you can’t really add or divide the values.

Range (spread of the data)

  • The range shows how spread out the data is.
  • Formula:

Range=largest value−smallest value\text{Range}=\text{largest value}-\text{smallest value}Range=largest value−smallest value

  • Example: For 3, 8, 10, 15, the smallest is 3 and the largest is 15, so the range is 15−3=1215-3=1215−3=12.

The range is the simplest measure of spread: a big range means the numbers vary a lot; a small range means they’re packed closer together.

All four together (quick example)

Take the numbers: 4, 4, 5, 7, 10.

  • Mean: (4+4+5+7+10)÷5=30÷5=6(4+4+5+7+10)÷5=30÷5=6(4+4+5+7+10)÷5=30÷5=6.
  • Median: The middle value in order is 5.
  • Mode: 4 (it appears twice, more than any other number).
  • Range: 10−4=610-4=610−4=6.

These four measures together give a quick “snapshot” of a data set: where its center is (mean, median, mode) and how wide it spreads (range).

TL;DR:

  • Mean = add and divide.
  • Median = middle value.
  • Mode = most frequent value.
  • Range = biggest minus smallest.