Review of Elementary Statistics – Unit 1

Flashcards cover definitions, classifications, formulas, and procedures from Unit 1: Review of Elementary Statistics, Lesson 1.1 and Lesson 1.2.

What is the general definition of Statistics?

The science of conducting studies to collect, organize, analyze, and draw conclusions from data.

From which Latin word is the term “Statistics” derived and what does it mean?

It comes from the Latin word status, meaning “state.”

Which branch of statistics summarizes and describes data for easier interpretation?

Descriptive statistics.

Which branch of statistics involves making generalizations or predictions about a population based on a sample?

Inferential statistics.

Give an example of descriptive statistics.

Reporting that the average height of the varsity team is 173 cm.

Give an example of inferential statistics.

Estimating future COVID-19 cases based on current Department of Health data.

Define population in statistical terms.

The entire set of individuals or entities of interest in a study.

Define sample in statistical terms.

A subset of the population selected to represent that population.

What is a parameter?

A numerical measurement that describes a characteristic of a population.

What is a statistic (as opposed to Statistics)?

A numerical measurement describing a characteristic of a sample.

State the relationship between sample statistics and population parameters.

Sample statistics are used as estimates of population parameters.

Define a variable.

A characteristic or attribute that can assume different values among individuals or entities.

Differentiate qualitative and quantitative variables.

Qualitative variables are categorical/non-numerical; quantitative variables are numerical and countable or measurable.

What are discrete quantitative variables?

Countable numerical values, e.g., number of students in a class.

What are continuous quantitative variables?

Measurable numerical values that can include fractions/decimals, e.g., height.

What is an independent variable?

The predictor or manipulated variable in an experiment.

What is a dependent variable?

The outcome variable that is measured and expected to change due to the independent variable.

Identify the independent and dependent variables: fertilizer amount vs. plant height.

Independent: amount of fertilizer; Dependent: plant height.

List the four levels of measurement.

Nominal, Ordinal, Interval, Ratio.

Describe nominal level of measurement.

Categorical data with no intrinsic ordering, e.g., gender or brand names.

Describe ordinal level of measurement.

Categorical data that can be ranked but with unknown intervals, e.g., class honors.

Describe interval level of measurement.

Numeric data with equal intervals but no true zero, e.g., temperature in °C.

Describe ratio level of measurement.

Numeric data with equal intervals and a true zero, e.g., weight.

How do you quickly distinguish interval from ratio data?

Check if zero represents absence of the quantity; if yes, it is ratio; if no, it is interval.

Name six common data-collection methods.

Direct/Interview, Indirect/Questionnaire, Registration, Observation, Experimentation, Use of Documents.

Differentiate primary and secondary data.

Primary data are first-hand (e.g., surveys); secondary data are obtained from existing sources (e.g., journals).

Name three broad methods of data presentation.

Textual, Tabular, Graphical.

What is a frequency distribution table (FDT)?

A statistical table that shows the number of observations (frequencies) for defined classes or categories.

List the basic parts of a frequency distribution table.

Table heading, body, caption, classes/stubs.

What are the two types of FDT?

Qualitative FDT and Quantitative FDT.

Formula for the range of a data set.

Range = Highest value − Lowest value.

How do you determine the minimum number of classes (k)?

k = √N, where N is the total frequency, rounded up to the nearest whole number.

Formula for class size (c).

c = Range ÷ k (rounded appropriately).

Define class mark.

The midpoint of a class interval, found by averaging the lower and upper limits.

Define true class boundaries (TCB).

Values that separate classes, found by subtracting/adding 0.5 (for whole numbers) to class limits.

What is cumulative frequency (<cf)?

Running total of frequencies from the lowest class upward.

What is relative frequency (RF) and its formula?

Percentage of a class frequency relative to total frequency; RF = (f / N) × 100%.

What is relative cumulative frequency (<RCF)?

Percentage version of cumulative frequency: (<cf / N) × 100%.

Name seven common graphs/charts used to present data.

Line chart, Pie chart, Column/Bar graph, Scatter graph, Frequency histogram, Frequency polygon, Ogive.

When is a line chart most useful?

When showing trends over time.

What type of chart best shows parts of a whole?

Pie chart.

What graph is specifically used for quantitative continuous data in classes?

Frequency histogram.

How is a frequency polygon constructed?

Plot frequencies at class marks and connect points with straight lines.

What is an ogive used for?

Displaying cumulative frequencies against true class boundaries to analyze medians and percentiles.

Why is it important to know a variable’s level of measurement?

Because it dictates which statistical tests and summary measures are appropriate.