Study guides › P/S › Research Methods & Statistics
Descriptive Statistics & Distributions
Descriptive statistics summarize a data set. You will calculate and compare mean, median, mode, and standard deviation, use the normal curve and z-scores, recognize skew, interpret correlation coefficients and scatterplots, and read the common graphs found in MCAT passages.
Study this chapter in PrepMed (free)
What this chapter covers
- Central Tendency & Variability. Passages report a center and a spread. You need to compute both quickly and know which one an outlier distorts.
- The Normal Distribution, Z-Scores & Percentiles. The bell curve and its 68-95-99.7 rule turn many MCAT statistics questions into simple mental arithmetic.
- Skew, Modality & the Shape of Data. The shape of a distribution tells you where the mean, median, and mode sit and which one to trust.
- Correlation & Scatterplots. A correlation coefficient compresses a scatterplot into one number. The MCAT tests both reading that number and not over-reading it.
- Reading Graphs & Data Displays. Half the difficulty of passage questions is reading the figure correctly: axes, error bars, and what the display can and cannot show.
Key points to know
- Mean is pulled by outliers; median and mode are not
- SD is the square root of variance and has the original units
- 68% within 1 SD, 95% within 2 SD, 99.7% within 3 SD
- z = (x − mean)/SD; positive above the mean, negative below
- Skew is named for the tail direction
- Positive skew: mean > median > mode; negative skew: mean < median < mode
- r ranges from −1 to +1; sign is direction, magnitude is strength
- r² is the fraction of variance shared
Try a practice question
Which measure of center is least affected by a single extreme outlier?
- Median
- Mean
- Range
- Variance
Show the answer
A. The median depends only on the middle position, so one extreme value barely moves it. The mean uses every value, and range and variance also respond strongly to outliers.
Common questions
What does this chapter cover?
Descriptive Statistics & Distributions covers Central Tendency & Variability, The Normal Distribution, Z-Scores & Percentiles, Skew, Modality & the Shape of Data, Correlation & Scatterplots, Reading Graphs & Data Displays.
What should I know first?
Mean is pulled by outliers; median and mode are not SD is the square root of variance and has the original units 68% within 1 SD, 95% within 2 SD, 99.7% within 3 SD
25 original practice questions accompany this chapter in the app. Spaced review brings missed ideas back at the right time; it helps memory but cannot promise you will not miss an idea again.