Statistics & Probability Descriptive Statistics & Data Exploration Syllabus

Descriptive Statistics & Data Exploration syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Descriptive Statistics & Data Exploration in Statistics & Probability, not a summary of it.

1. 1

   Types of Data and Measurement

   4 topics

   • Population vs Sample
   • Variable Types
   • Levels of Measurement
   • Data Collection Methods
2. 2

   Measures of Central Tendency

   4 topics

   • Mean
   • Median
   • Mode
   • Choosing the Right Measure
3. 3

   Measures of Dispersion

   4 topics

   • Range and Interquartile Range
   • Variance and Standard Deviation
   • Coefficient of Variation
   • Mean Absolute Deviation
4. 4

   Shape and Position

   4 topics

   • Skewness
   • Kurtosis
   • Percentiles and Quantiles
   • Z-Scores and Standardization
5. 5

   Data Visualization

   5 topics

   • Histograms and Frequency Distributions
   • Box Plots and Outlier Detection
   • Bar Charts and Pie Charts
   • Scatter Plots
   • Stem-and-Leaf and Dot Plots
6. 6

   Exploratory Data Analysis

   4 topics

   • Five-Number Summary
   • Identifying Patterns and Trends
   • Handling Missing Data
   • Detecting and Treating Outliers

Descriptive Statistics & Data Exploration flashcards for Statistics & Probability

20 of 51 cards from the Descriptive Statistics & Data Exploration deck — real questions with worked answers.

1. What is a population in statistics?

   The entire set of all individuals, items, or events of interest about which we want to draw conclusions.

2. What is a sample?

   A subset of the population selected for measurement and analysis, used to make inferences about the whole population.

3. Distinguish a parameter from a statistic.

   A parameter is a numerical characteristic of a population (e.g. $\mu$, $\sigma$); a statistic is a numerical characteristic computed from a sample (e.g. $\bar{x}$, $s$).

4. What is the difference between qualitative (categorical) and quantitative (numerical) variables?

   Qualitative variables describe categories or labels (e.g. color, gender); quantitative variables represent measurable numeric quantities (e.g. height, count).

5. Distinguish discrete from continuous quantitative variables.

   Discrete variables take countable, separate values (e.g. number of children); continuous variables can take any value within an interval (e.g. weight, time).

6. Name the four levels of measurement in order of increasing information.

   Nominal, ordinal, interval, and ratio.

7. What defines the nominal level of measurement?

   Data are labels or categories with no inherent order and no arithmetic meaning (e.g. eye color, nationality).

8. What defines the ordinal level of measurement?

   Categories have a meaningful order or ranking, but the differences between values are not necessarily equal or meaningful (e.g. survey ratings, class rank).

9. What distinguishes the interval level from the ratio level of measurement?

   Interval data have equal spacing but no true zero (e.g. Celsius temperature), so ratios are meaningless; ratio data have equal spacing and a true zero (e.g. mass, length), so ratios are meaningful.

10. What is the difference between a census and a sample survey?

    A census collects data from every member of the population; a sample survey collects data from only a selected subset.

11. What is simple random sampling?

    A sampling method in which every member of the population has an equal and independent chance of being selected.

12. Contrast an observational study with a designed experiment.

    In an observational study the researcher measures variables without intervening; in an experiment the researcher deliberately manipulates one or more variables (treatments) to observe the effect.

13. State the formula for the sample mean of $n$ observations.

    $$\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$$

14. State the formula for the population mean.

    $$\mu = \frac{1}{N}\sum_{i=1}^{N} x_i$$

15. How is the median of a data set defined and found?

    The median is the middle value when data are ordered. For odd $n$ it is the value at position $\frac{n+1}{2}$; for even $n$ it is the average of the two central values at positions $\frac{n}{2}$ and $\frac{n}{2}+1$.

16. What is the mode of a data set?

    The value (or values) that occurs most frequently. A distribution may be unimodal, bimodal, multimodal, or have no mode.

17. Which measure of central tendency is most resistant to outliers, and why?

    The median, because it depends only on the rank/position of the middle value(s), not on the magnitude of extreme values.

18. In a right-skewed (positively skewed) distribution, how do the mean, median, and mode typically compare?

    $\text{mode} < \text{median} < \text{mean}$; the mean is pulled toward the long right tail.

19. Which measure of central tendency is appropriate for nominal data?

    Only the mode, since nominal categories cannot be ordered or averaged.

20. How is the range of a data set calculated?

    $$\text{Range} = x_{\max} - x_{\min}$$

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