How to Master Descriptive Statistics: 108 Flashcards on Mean, Median, Mode and Standard Deviation
Learn descriptive statistics with 108 flashcards: mean, median, mode, variance, standard deviation, z-scores, IQR, skewness and Pearson correlation.
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The mean tells you where a dataset sits. The standard deviation tells you whether that number means anything at all. Descriptive Statistics: Mean, Median, Mode & Standard Deviation (code IN3111, 108 cards) on Flip It drills the definitions, formulas and symbols that AP Statistics, intro stats and data-analysis courses assume you already know cold.
Study this deck: Descriptive Statistics: Mean, Median, Mode & Standard Deviation
1 / 10Descriptive statistics
Tap the card for the answer · swipe right if you knew it, left if not
A sample of what the cards ask:
| Front | Back |
|---|---|
| Sample standard deviation formula | s = √[Σ(x − x̄)² / (n−1)], using Bessel's correction (n−1) for unbiased estimation |
| Why use (n−1) instead of n in sample standard deviation? | Bessel's correction provides an unbiased estimate of the population variance from a sample |
| Interquartile range (IQR) | IQR = Q3 − Q1, the range of the middle 50% of data, robust to outliers |
| Z-score (standard score) | z = (x − μ)/σ, the number of standard deviations a value is from the mean |
| Chebyshev's inequality | At least (1 − 1/k²) of data lies within k standard deviations of the mean, for any distribution |
| Coefficient of variation | CV = (σ/μ) × 100%, the ratio of standard deviation to mean, useful for comparing variability across different scales |
| Common rule for identifying outliers | Values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR |
| Standard error of the mean | SEM = σ/√n, the standard deviation of the sampling distribution of the mean |
| Positive skewness | When the tail on the right side is longer (mean > median) |
| Leptokurtic kurtosis | Heavy tails and a sharp peak (high kurtosis) |
The 108 cards in one glance
- Centre: arithmetic mean, median, mode, weighted mean, geometric mean, harmonic mean, truncated mean, mid-range, root mean square, the AM ≥ GM ≥ HM inequality, multimodal datasets.
- Spread: range, population and sample variance, both standard deviation formulas, mean absolute deviation, IQR, quartiles Q1–Q3, percentiles, coefficient of variation.
- Shape: skewness (right and left), kurtosis (leptokurtic, platykurtic, mesokurtic), the normal distribution, the empirical 68-95-99.7 rule, log transformation of skewed data.
- Position and standardisation: z-scores, five-number summary, outlier rules, Chebyshev's bounds at k = 2 (75%) and k = 3 (89%).
- Relationships: covariance, Pearson's r, Spearman's rho, r = +1 / −1 / 0, correlation versus causation, contingency tables, bivariate and multivariate analysis.
- Vocabulary and notation: population versus sample, μ and σ against x̄ and s, sampling error, standard error, frequency and cumulative frequency, relative frequency, EDA.
- Graphs: histogram, bar chart (and the difference), box plot, stem-and-leaf display, scatterplot, pie chart.
Two things worth doing while you review
Keep the μ/σ and x̄/s cards side by side. Roughly a fifth of the deck exists only because population and sample formulas differ. Every time a variance or standard deviation card comes up, say out loud whether you are dividing by N or by n−1 before flipping. Exam questions rarely test the arithmetic — they test whether you noticed the word sample.
Pair the empirical rule with Chebyshev. The cards give 68/95/99.7 for normal data and 75%/89% for any distribution. Learn them as a matched pair: if the question mentions a bell curve, use the first set; if it says nothing about shape, only Chebyshev's weaker bound is defensible.
Sign in at flip-it.app and search the library for deck IN3111. If you want the visual side of data next, try Pandas Essentials, which puts these same summaries into code.
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