Ch. 1. Descriptive Statistics
I. Central Tendency: Center of a distribution
A. Mode: the most frequently occurring score(s).
1. Least useful in general.
2. We may have multiple modes
B. Median: the point that divides a distribution into
two parts so that half falls above the median and half
below.
1. If n is odd, use the middle score.
2. If n is even, use the mean of the two middle
scores.
3. For grouped data, use the interpolation formula.
4. If a distribution has extreme scores, the median
is more representative (stable) than the mean.
C. Mean: arithmetic average
_
1. μ = ΣX/N X = ΣX/n
2. The most stable statistic in most cases.
3. The mean is affected by extreme scores.
II. Variability: The degree of dispersion of scores, how
widely scores spread out in a distribution.
A. Range (ordered)
1. The highest score - the lowest score.
2. Very sensitive to extreme scores (outliers).
B. Quartiles (ordered)
1. First Quartile (lower hinge, Q1): separates the
lower 25% of a distribution.
Second Quartile Q2: separates the lower 50% of a
distribution.
Third Quartile (upper hinge, Q3): separates the
lower 75% of a distribution.
2. Interquartile range Q3-Q1 (H-spread).
3. Semi-interquartile range:
_
C. Sum of Squares (SS): Σ(X-X)²
Least Squares Principle
E. Variance
1. Population variance: σ²
2. Biased Sample Variance: s*²
3. Unbiased Sample Variance: s²
4. Standard deviations σ =
2
σ
, s* =
2
*s
, and
s =
2
s
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