LEMMA

Measurement & data

Mode, range, and medians

TEAS math

Mode is the most frequent value, range is the spread, and an even count averages its two middles.

What this covers

range=max−min,medianeven​=2m1​+m2​​
  • Sort the data before anything else — it makes every measure visible.
  • Mode: the value that appears most often, not how often it appears.
  • Range: largest minus smallest — a distance, not a value from the list.
  • Even count: no single middle exists, so average the two middle values.

Worked example

Worked example

Find the median of 82, 74, 90, 78, 86, 70.

  1. 70, 74, 78, 82, 86, 90Sorting first makes the middle findable.
  2. 278+82​=80Six values have two middles; the median is halfway between them.
Another worked example

Find median, range, and mode of 1, 2, 3, 4, 5, 6, 7, 8.

  1. median=24+5​=4.5With eight observations, average the fourth and fifth values.
  2. range=8−1=7;no modeAll values occur once, so none occurs more frequently under the convention used here.

A common mistake

A mistake Lemma catches

From 70, 74, 78, 82, 86, 90

median=78median=278+82​

“Six values have two middle values, the 3rd and the 4th: 78 and 82. The median is their mean: (78 + 82)/2 = 80. Taking just 78 uses only one of them.”

Try one

Sample problem

Patients rated their pain as 6, 9, 5, 9, 6, 9. What is the mode? Enter the number.

6, 9, 5, 9, 6, 9

Practice data shapes 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