Unit 1: Exploring One-Variable Data

Question 1

Categorical Variable/Qualitative Data

Answer 1

A variable that takes on values that are category names or group labels. (Think: WORDS)
(EX: Dominant hand, name, college degree)

Question 2

Quantitative Variable/Data

Answer 2

A variable that takes on numerical values for a measured or counted quantity. (Think: NUMBERS)
(EX: Age, height, count)
Can be discrete or continuous

Question 3

Frequency table

Answer 3

gives the number of cases in each category

Question 4

Relative frequency table

Answer 4

gives the proportion of cases in each category(percentage)
[Note: percentage, relative frequency, and rates provide the same information as proportions]

Question 5

Bar Chart/Graph

Answer 5

A graph to display counts or proportions for a categorical variable only

Question 6

Pie Chart

Answer 6

A chart to display proportions

Question 7

Discrete Quantitative Variable

Answer 7

A variable that can take on a countable(finite or countably infinite) number of values.

Question 8

Continuous Quantitative Variable

Answer 8

A variable that can take on infinitely many values, but those values cannot be counted.

Question 9

Dot Plots

Answer 9

Best for discrete variables

Question 10

Steam and Leaf plots

Answer 10

Stem: the number(s) on the left of the plot and the number (EX: stem of 34 is 3)
Leaf: the number on the right of the plot and the number (EX: leaf of 34 is 3)

Question 11

Histogram

Answer 11

[NOT a bar graph]
gives a discrete Y-value but a continuous X-axis due to the bars connecting.

Question 12

Population

Answer 12

The collection of all individuals or items under consideration in a statistical study

Question 13

Sample

Answer 13

part of a population

Question 14

Inferential statistics

Answer 14

Drawing and measuring the reliability of conclusions about a population based on information obtained from a sample of the population

Question 15

Skewed Right

Answer 15

More data on the right with a left tail

Question 16

Skewed Left

Answer 16

More data on the left with a right tail

Question 17

Symmetric Data

Answer 17

A distribution that is symmetric (peak in middle(unimodal) or peaks on each side(bimodal))

Question 18

uniform data

Answer 18

The data is all the same

Question 19

census

Answer 19

Information for the entire population of interest.

Question 20

Sampling

Answer 20

How to obtain an appropriate subset of people/items from the population. There are 2 types.

Question 21

[SRSWR] Simple random sampling with replacement

Answer 21

Where a member of the population
can be selected more than once

Question 22

[SRS] Simple random sampling without replacement

Answer 22

Where a member of the population can be selected at most once.

Question 23

Statistic vs Parameter

Answer 23

Statistic: value from sample
Parameter: value from population

Question 24

Systematic Random Sampling

Answer 24

Elements from a larger population are selected at regular intervals after choosing a random starting point.

Question 25

Cluster Sampling

Answer 25

A population is divided into groups/clusters, and entire clusters are randomly selected for study. Often used when a population is too large or widely spread out for SRS.

Question 26

Stratified Sampling

Answer 26

A population is divided into subgroups (strata) based on a shared characteristic, and then a random sample is taken from each stratum. Focus on the representation of groups.

Question 27

Mean X̅

Answer 27

Average of a dataset Affected by outliers Will move towards the tail in a skewed graph

Question 28

Median

Answer 28

Middle value of an ordered dataset AKA 2nd Quartile Not affected by outliers [Formula: (n+1)/2]

Question 29

Percentile

Answer 29

Percent of data values less than or equal to a certain value EX: The p-th percentile means that p% of the data falls below that value.

Question 30

Standardized Score / Z-Score

Answer 30

A measure of how many standard deviations a data point is from the dataset of any shape(not exclusive to normal distribution)

Question 31

Normal Distribution

Answer 31

Bell-curved Middle is the μ σ standard deviations Emperical rule(68%-95%-99.7% rule)

Question 32

How to read a Z-score table

Answer 32

Y-Axis: Ones and tenths place of z-score X-Axis: hundredths place of z-score The result shows the percentage area of the distribution.

Question 33

Skewed Right/Positive Shape Properties

Answer 33

Right tail Highest bar on the left Mean > Median

Question 34

Skewed Left/Negative Shape Properties

Answer 34

Left tail Highest bar on the right Mean < Median

Question 35

Symmetrical Shape Properties

Answer 35

Highest bar in the middle Mean ≈ Median ≈ Mode

Question 36

Mean formula

Answer 36

x̄ = Σxᵢ / n

Question 37

Median formula

Answer 37

Middle of data

Question 38

Range formula

Answer 38

Max - Min

Question 39

IQR formula

Answer 39

IQR = Q₃ − Q₁

Question 40

Outlier rule

Answer 40

Outlier IF: x < Q₁ − 1.5×IQR OR x > Q₃ + 1.5×IQR

Question 41

Standard deviation (sample) formula

Answer 41

s: sample standard deviation xᵢ: any possible outcomes x̄: Sample mean s = √[ (Σ(xᵢ − x̄)²) / (n − 1)]

Question 42

Z-score formula

Answer 42

x: random variable z = (x - μ) / σ

Question 43

Chebyshev's Theorem

Question 44

Empirical Rule

Answer 44

A rough estimate of the standard deviation s ≈ range / 4

Question 45

SOCS

Answer 45

Shape, Outliers, Center, Spread

Question 46

Socs

Answer 46

Shape: Symmetric, Skewed, Uniform, and Bell-shaped

Question 47

sOcs

Answer 47

Outliers: values outside of an overall pattern

Question 48

soCs

Answer 48

Center: The median or mean of a curve

Question 49

socS

Answer 49

Spread/variability: scope of values from smallest to largest

Question 50

Cluster

Answer 50

A subgroup of which values fall into based on category(age range, school, sex, tax rate)