Free video lesson

How to Tell Mean From Median on the SAT

Change one number and the mean can swing wildly — while the median doesn't flinch. This is the outlier trap the SAT loves, and knowing which measure to trust is free points.

Math · One-variable data: center & spread2:10Published July 5, 2026

On YouTube: SAT Statistics: Mean ≠ Median

What this lesson covers

  • Median = the middle value (position); mean = the balance point of the data
  • Add one outlier: the mean lurches, the median holds
  • When data is skewed, the median is the honest "typical" value
  • Practice: 1, 2, 2, 3, 92 — mean or median?
  • The three traps that cost easy points

Questions worked in the video

  1. 0:29The data 3, 5, 6, 7, 8, 9, 11 — find the mean and median. What if 11 becomes 60?
  2. 1:09For 1, 2, 2, 3, 92 — find the mean and median. Which better describes the group?

Worked examples

The questions the video works, written out: the setup, each step, the answer and the trap.

0:29Example 1

The data set is 3, 5, 6, 7, 8, 9, 11. Find the mean and the median. Then suppose the 11 is changed to 60. What happens to each measure?

  1. Mean: add the seven values, 3+5+6+7+8+9+11=493 + 5 + 6 + 7 + 8 + 9 + 11 = 49, then divide by how many there are: 497=7\displaystyle \frac{49}{7} = 7.
  2. Median: the list is already in order, and with seven values the middle is the 4th one. Counting in: 3, 5, 6, then 7. The median is 7. Right now the two measures agree.
  3. Swap 11 for 60. The new sum is 49−11+60=9849 - 11 + 60 = 98, so the new mean is 987=14\displaystyle \frac{98}{7} = 14. It doubled.
  4. The new list in order is 3, 5, 6, 7, 8, 9, 60. The 4th value is still 7, so the median has not moved.
  5. Check: seven values with a mean of 14 should total 7×14=987 \times 14 = 98, and they do.

Answer: Originally mean = 7 and median = 7; after the change mean = 14 and median = 7

The mean is the balance point of the data, so one far value drags it toward itself, while the median only cares which value sits in the middle position, and the 60 is still just one value at the top end. The trap is expecting the median to jump too. A student who re-adds the list to find the new median also wastes time; the median needed no arithmetic at all.

1:09Example 2

For the data 1, 2, 2, 3, 92, find the mean and the median. Which one better describes a typical value in the group?

  1. Mean: 1+2+2+3+92=1001 + 2 + 2 + 3 + 92 = 100, and 1005=20\displaystyle \frac{100}{5} = 20.
  2. Median: five values, already sorted, so the middle is the 3rd: 1, 2, then 2. The median is 2.
  3. Compare them to the data. Four of the five values are 3 or less, so a typical value is about 2. The mean of 20 is bigger than every value except the outlier.
  4. Check: 5×20=1005 \times 20 = 100 matches the sum, and without the 92 the other four values average 84=2\displaystyle \frac{8}{4} = 2, right on the median.

Answer: mean = 20, median = 2; the median describes the group

The single value 92 inflates the mean to 20, a number nothing in the group is close to, while the median stays with the cluster at 2. When the SAT asks which measure better represents skewed data, or which measure changes more when an outlier is added or removed, the median is the stable one. The trap is grabbing a middle value before sorting; this list happens to be sorted, but on the test it usually is not.

Chapters

Lesson transcript

The narration of the video, word for word, under its chapter headings.

0:00The average can lie

Welcome to SAT Climb. The average can lie. Change one number, and the mean swings wildly — while the median doesn't flinch. Knowing which is which is free points.

0:16The setup: seven numbers

Seven numbers. Add them up, divide by 7 — that's the mean, 7. Line them up, take the middle — that's the median, also 7. Right now they agree.

0:29Median vs mean, pictured

The median is the middle value — position, not size. The mean is the balance point: where the line tips level. With no outlier, both say 7.

0:49Add one outlier

Now one value jumps to 60 — an outlier. The balance point chases it: the mean doubles to 14. But the median? Still the 4th number. Still 7. Outliers drag the mean and leave the median alone.

1:09Your turn

Your turn. 1, 2, 2, 3, 92. Find the mean and the median — then decide which one actually describes the group.

1:35Three traps

Three traps. With a skew, the median is honest, not the mean. A far value barely moves the median. And sort before you take the middle.

1:56Recap

Mean, median: solved. Spot the outlier, and you know which measure the test is really after. Start free at satclimb.com.

Read the written version: the One-variable data: center & spread strategy guide, then try 25 hard One-variable data: center & spread questions with full explanations. Both are free, no account needed.

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