LEMMA

Measurement & data

Mean, median, and spread

TEAS math

Mean shares the total out equally; median is the middle of the sorted list.

What this covers

mean=how manysum of values​
  • For the mean, add every value and divide by how many values there are.
  • For the median, sort first, then take the middle value.
  • With an even count, the median is halfway between the two middle values.
  • Range is largest minus smallest, and mode is the value that appears most often.

Worked example

Worked example

Find the mean and median of 82, 74, 90, 74, 80.

  1. 582+74+90+74+80​=80Five values total 400, shared equally that is 80 each.
  2. 74, 74, 80, 82, 90 ⇒ 80Sorted, the third of five values is the median.
Another worked example

Find the mean and median of 2, 3, 3, 4, 30.

  1. xˉ=52+3+3+4+30​=542​=8.4Every observation contributes to the total used by the mean.
  2. median=3The third value remains the middle of this sorted five-value list.

A common mistake

A mistake Lemma catches

From

xˉ=280+90​xˉ=53⋅80+2⋅90​

“80 counts three times and 90 twice, so the mean weights them: (3 · 80 + 2 · 90)/5 = 420/5 = 84. Averaging just the two scores, (80 + 90)/2 = 85, treats each as a single quiz.”

Try one

Sample problem

Five test scores are 77, 78, 79, 80, 81. What is the mean score? Enter the number.

577+78+79+80+81​

Practice statistics free

No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.

Where this fits

Before this

After this