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Descriptive Statistics
Descriptive Statistics
Descriptive statistics summarize the main features of a data set.
Measures of Center
- Mean: arithmetic average
- Median: middle value
- Mode: most frequent value
Measures of Spread
- Range: max minus min
- Variance: average squared deviation
- Standard deviation: square root of variance
- IQR: $Q_3-Q_1$
Example 1
Find the mean of $2,4,6,8$.
$\frac{20}{4}=5$.
Example 2
Find the median of $1,3,3,9,10$.
The middle value is $3$.
Example 3
Find the range of $4,7,9,11$.
$11-4=7$.
Practice Problems
1. Mean of $5,7,8$
2. Median of $2,4,8,10$
3. Mode of $1,2,2,2,5$
4. Range of $12,18,21$
5. When is median preferred over mean?
Show Answer Key
1. $\frac{20}{3}$
2. $6$
3. $2$
4. $9$
5. When data contain outliers or are skewed