One snack, two different answers
The mean adds all the values and divides by how many there are. The median is the middle value after you put them in order. With an even number of values, take the mean of the two middle ones. OpenStax explains both measures.
Imagine five friends bringing biscuits to a picnic: 2, 3, 3, 4 and 18. Four pack a small snack. One arrives with a tin that means business. How many biscuits did a typical friend bring?
Share the whole pile
Add the five amounts: 2 + 3 + 3 + 4 + 18 = 30. Divide by five friends: 30 ÷ 5 = 6. The mean is six biscuits.
Think of it as sharing the total equally. Everyone would get six if the friends pooled their biscuits. Nobody actually brought six. That does not make the calculation wrong; it tells you what the mean measures.
Pick the middle friend
The amounts are already in order: 2, 3, 3, 4, 18. The third value sits in the middle, so the median is three biscuits.
Now imagine the generous friend brings 38 instead of 18. The total becomes 50, so the mean rises to 10. The middle value is still 3. A very large value can pull the mean upwards without changing the median in this example. OpenStax discusses this effect of extreme values.
Which answer should you use?
Want to know what everyone could receive after sharing? The mean answers that question. Want to describe the middle of this rather uneven group? The median is useful.
For an even-sized group, try 2, 3, 4, 9. The middle pair is 3 and 4. Their mean is (3 + 4) ÷ 2 = 3.5, so the median is 3.5. It need not be a number anyone brought.
When you hear “the average”, ask which average it means. The biscuits have not changed. The question has.