Descriptive Statistics

Question 1

Define parameter vs statistic.

Answer 1

Parameter = measure of a population characteristic.
Statistic = measure of a sample characteristic.

Question 2

What are descriptive vs inferential statistics?

Answer 2

Descriptive = summarize and describe data.
Inferential = draw conclusions from a sample to a population.

Question 3

What are numerical variables?

Answer 3

Variables measured on an interval or ratio scale (e.g., height, weight, percent grade).

Question 4

Differentiate discrete and continuous numerical variables.

Answer 4

Discrete = finite numbers (10 students).
Continuous = any value on a range (height = 170.5 cm).

Question 5

What graphs are used for categorical data?

Answer 5

Bar plots and pie charts.

Question 6

What graphs are used for numerical data?

Answer 6

Histograms and box plots.

Question 7

Why use descriptive statistics and graphs?

Answer 7

They help visualize patterns, outliers, and data distribution before making inferences.

Question 8

Measures of central tendency

Answer 8

mean, median, mode

Question 9

Measures of spread

Answer 9

range, interquartile range, standard deviation

Question 10

Measures of position

Answer 10

percentiles, deciles, quartiles, median

Question 11

Define mean.

Answer 11

Arithmetic average

Question 12

Define median.

Answer 12

Midpoint where half of scores lie above and half below.

Question 13

Define mode.

Answer 13

Most frequently occurring value — best for categorical data.

Question 14

Which measure is affected by outliers?

Answer 14

Mean

Question 15

Which measure best describes skewed distributions?

Answer 15

Median (less sensitive to extremes).

Question 16

Characteristics of a normal distribution?

Answer 16

Bell-shaped, symmetrical, mean = median.

Question 17

Right (positive) skew vs left (negative) skew?

Answer 17

Right → mean > median. Left → mean < median.

Question 18

Define range.

Answer 18

Difference between highest and lowest values (max – min).

Question 19

Define standard deviation (SD).

Answer 19

Average distance of each score from the mean.

Question 20

Define interquartile range (IQR).

Answer 20

Distance between Q1 (25th percentile) and Q3 (75th percentile); represents middle 50% of data.

Question 21

How is variance related to standard deviation?

Answer 21

Variance = SD².

Question 22

Formula for Z score?

Answer 22

Z = (X – μ) / σ.

Question 23

What does a Z score represent?

Answer 23

Number of standard deviations a value is above (+z) or below (–z) the mean.

Question 24

What is the 68–95–99% rule?

Answer 24

68% within ±1 SD, 95% within ±2 SD, 99% within ±3 SD of mean.

Question 25

What are percentiles?

Answer 25

Values below which a certain percent of data fall (e.g., 25th = lower 25%).

Question 26

What are quartiles?

Answer 26

Values that divide data into four equal parts (Q1, Q2, Q3, Q4).

Question 27

What is the IQR?

Answer 27

Q3 – Q1; represents middle 50% of data, excluding extremes.

Question 28

Best descriptive measures for categorical data?

Answer 28

Proportions and frequencies.

Question 29

For normally distributed data, what measures should be reported?

Answer 29

Mean (central tendency) and SD (variability).

Question 30

For skewed data, what measures are better?

Answer 30

Median (central tendency) and IQR (or 5th–95th percentiles for spread).