TEAS Ready📏 Math · Measurement and Data · Lesson 2 of 7 · 5 min
Mean, median, mode and range
🧮 Four quick numbers sum up any list: its average, its middle, its most common value and its spread.
💡 Key idea
Mean = sum ÷ count; median = middle of the sorted list; mode = most frequent; range = max − min.
🧠 The idea
The MEAN is the average: add all the values and divide by how many there are. The MEDIAN is the middle value after you put the list in order; with an even number of values, it is the mean of the two middle values. The MODE is the value that appears most often; a list can have no mode or more than one. The RANGE is the largest value minus the smallest. A common TEAS twist asks for a missing value: if you know the target mean, multiply it by the number of values to get the needed total, then subtract the values you already have. Always sort before finding the median; the most common mistake is picking the middle of an unsorted list.
✏️ Worked example
A student's quiz scores are 78, 85, 92 and 81. What score on a fifth quiz would make the mean exactly 85?
Step 1: Needed total = target mean × number of quizzes = 85 × 5 = 425.
Step 2: Current total = 78 + 85 + 92 + 81 = 336.
Step 3: Missing score = 425 − 336 = 89.
Check: (336 + 89) ÷ 5 = 425 ÷ 5 = 85. ✓
Answer: the student needs an 89.
📌 Takeaways
- Sort the list before finding the median.
- Even count: the median is the average of the two middle values.
- Missing value = target mean × count − current sum.
📖 Terms in this lesson
Mean: The sum of the values divided by how many values there are; for example, the mean of 4, 6 and 8 is 18 ÷ 3 = 6.
Median: The middle value when data are in order (the mean of the two middle values if the count is even); for example, the median of 2, 5, 9 is 5.
Mode: The value that appears most often in a data set; for example, the mode of 3, 4, 4, 7 is 4.
Range: The highest value minus the lowest value; for example, the range of 10, 15 and 22 is 12.
✅ Check yourself
Question 1 of 3
What is the mean of 4, 8, 6, 10 and 7?
- 7
- 35
- 6
- 8
Show the answer and rationale
Answer: A
Sum = 4 + 8 + 6 + 10 + 7 = 35, and 35 ÷ 5 = 7. Thirty-five is the sum before dividing, 6 is the middle of the unsorted list, and 8 is just one of the values.
Question 2 of 3
What is the median of 3, 9, 4, 12, 7 and 5?
- 7
- 5.5
- 6
- 6.7
Show the answer and rationale
Answer: C
Sorted: 3, 4, 5, 7, 9, 12. The two middle values are 5 and 7, so the median is (5 + 7) ÷ 2 = 6. About 6.7 is the mean, 7 is only one of the middle values, and 5.5 averages 4 and 7 instead of the two middle values.
Question 3 of 3
A student scored 80, 85 and 90 on three tests. What score on the fourth test gives a mean of 88?
- 97
- 88
- 352
- 95
Show the answer and rationale
Answer: A
Needed total = 88 × 4 = 352. Current total = 80 + 85 + 90 = 255. Missing score = 352 − 255 = 97. Scoring 88 would give a mean of only 343 ÷ 4 = 85.75, 95 falls short of the 352 total, and 352 is the needed total, not the fourth score.
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