TEAS Ready📏 Math · Measurement and Data · Lesson 3 of 7 · 5 min
Spread, outliers and the shape of data
📈 Two classes can have the same average and look nothing alike. Spread and shape tell you the rest of the story.
💡 Key idea
Outliers and skew drag the mean toward the tail, so the median is the better 'typical' value for lopsided data.
🧠 The idea
SPREAD describes how far apart the values are. The range is the simplest measure; a larger range means the data are more spread out. An OUTLIER is a value far from the rest, such as 61 in the list 22, 24, 25, 23, 61. Outliers pull the mean toward them but barely move the median, so when data contain outliers or are lopsided, the median is the better summary of a typical value. SHAPE describes the overall pattern. A symmetric (bell-shaped) distribution has mean and median close together. A distribution that is SKEWED RIGHT has a long tail of high values, and its mean is greater than its median; skewed left has a tail of low values, and its mean is less than its median. Clustered data have little spread; data with a gap or two peaks may come from two different groups.
✏️ Worked example
Five nurses' commute times are 12, 15, 14, 13 and 66 minutes. Which measure better describes a typical commute?
Step 1: Mean = (12 + 15 + 14 + 13 + 66) ÷ 5 = 120 ÷ 5 = 24 minutes.
Step 2: Sort: 12, 13, 14, 15, 66. Median = 14 minutes.
Step 3: Compare. Four of five nurses commute 12–15 minutes; 66 is an outlier that pulled the mean up to 24.
Answer: the median, 14 minutes, better describes a typical commute.
📌 Takeaways
- An outlier is far from the rest; it moves the mean much more than the median.
- Skewed right: mean > median. Skewed left: mean < median.
- Bigger range = more spread out data.
📖 Terms in this lesson
Outlier: A value far from the rest of the data that can pull the mean toward it; for example, 95 in the set 10, 12, 11, 95.
✅ Check yourself
Question 1 of 3
Which value is an outlier in the data set 102, 104, 105, 103, 61?
- 61
- 102
- 95
- 105
Show the answer and rationale
Answer: A
Four values sit between 102 and 105, and 61 is far below them, so 61 is the outlier; an outlier can be unusually low as well as high. The values 102 and 105 are the ends of the main cluster, and 95 is the mean, not a data value.
Question 2 of 3
Home prices in a town include a few very expensive houses. Which measure best represents a typical home price?
- Mode of the prices
- Median
- Mean
- Range
Show the answer and rationale
Answer: B
A few very high prices skew the data right and pull the mean up, so the median gives a better typical value. The range measures spread, not center, and the mode may not exist when every price is different.
Question 3 of 3
Class A's scores range from 70 to 90; Class B's range from 50 to 100. Both have a mean of 80. Which statement is true?
- The two classes have exactly the same spread.
- Class A's scores are more spread out.
- Class B's scores are more spread out.
- Class B has a higher median.
Show the answer and rationale
Answer: C
Class B's range is 100 − 50 = 50, while Class A's is 90 − 70 = 20, so Class B is more spread out. Equal means do not imply equal spread, and nothing given tells us either median.
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