Stats Unit 1

What is descriptive statistics?

Organizing and summarizing data

What is inferential statistics?

Uses probability to determine how confident we can be that our conclusions are correct

What is the field of statistics used for?

Making decisions

What is a simple random sample?

Every sample of size n has an equal chance of being selected

What is probability?

How likely something is to occur

What is a population?

The group being described

What is a sample?

A subset of the population

What is sampling?

Selects a portion of the larger population and studies that portion to gain information about the population

What is a statistic?

Describes a characteristic of the sample

What is a parameter?

A numerical value that describes a characteristic of an entire population

What is a representative sample?

A small group chosen from a larger population that accurately mirrors the key characteristics of the population

What is a variable?

Usually notated by capital letters such as X and Y; it is a characteristic or measurement that can be determined for each member of a population

What are the types of variables?

Numerical and categorical

What is a numerical variable?

A characteristic that represents a measurable quantity or count

What is a categorical variable?

A data type that puts things into groups or categories. Math is not used for these values

What is a datum?

A single, individual piece of information, measurement, or observation. It is the singular form of the word data

What is qualitative data?

A type of categorical data that is non-numerical information that describes traits, labels, or characteristics

What is quantitative data?

Any information that can be counted, measured, and written down with numbers

What is quantitative discrete data?

Numerical information that you get by counting rather than measuring. It can only take specific, separated values—usually whole integers—with distinct gaps in between, meaning no fractions or decimals

What is quantitative continuous data?

Numerical information that you measure rather than count. It can take any value within a given range and can include fractions and decimals, meaning there is an infinite number of possible values

What is a Pareto chart?

Consists of bars that are sorted into order by category size (largest to smallest)

What is random sampling?

A statistical technique where a researcher selects a subset of individuals from a larger population by pure chance

What is a simple random sample?

Every sample of size n has an equal chance of being selected

What is a stratified sample?

A statistical method where you split a large group (population) into smaller, non-overlapping groups (called strata) based on shared traits like age or income. You then pick random samples from each small group. This makes sure every part of the population is fairly represented

What is a cluster sample?

A method where researchers split a large population into smaller, naturally occurring groups called clusters (such as cities, schools, or city blocks). They then pick a random sample of these clusters to study

What is a systematic sample?

Every Nth; a statistical method where researchers choose members of a population at a regular, fixed interval (k) after picking a random starting point

What is convenience sampling?

A non-probability data collection method where researchers select participants who are close at hand, easy to reach, or readily available. Common examples include polling students in a local classroom, asking people passing by on a street, or sharing an online survey on social media

What is sampling with replacement?

A method where each item you choose from a group is put back before you draw the next one. This means the same item can be picked more than once. Every pick is independent because the total group stays the same size

What is random sampling without replacement?

A member of the population may be chosen only once for the sample

What are nonsampling errors?

A statistical term for any mistake or bias that happens during data collection, recording, or processing, causing results to differ from the true population value

What are sampling errors?

The natural difference between a sample statistic (like a sample average) and the true population parameter (like the true population average). It happens simply because you study a small group instead of the whole group

What is sampling bias?

When some members of a group are much more likely to be picked for a study than others. This flaw makes the final sample different from the whole population. It leads to false results because the data favors one outcome

What is variation?

Measures how far apart the numbers in a data set are from each other and from their average (mean). It shows whether your data values are bunched closely together or spread out over a wide range

What is variability in samples?

When you take multiple random samples from the same population, the numerical summary values (like the mean or percentage) will differ from one sample to the next simply due to random chance

What is the number of observations?

The size of the sample

What is the level of measurement?

Tells us how variables are classified, ordered, or quantified, which determines what math and statistical tests you can use

What are the four levels of measurement from lowest to highest?

Nominal scale level; Ordinal scale level; Interval scale level; Ratio scale level

What is the nominal scale level?

The simplest measurement scale in statistics. It sorts data into distinct, named categories that have no natural order, rank, or numerical value. Example: colors, names, labels

What is a stem-and-leaf plot (stemplot)?

A graph that organizes data by separating each number into a stem and a leaf

When are stem-and-leaf plots most useful?

When the data set is relatively small

What is the leaf in a stem-and-leaf plot?

The final significant digit of a data value

What is the stem in a stem-and-leaf plot?

All of the digits of a data value except the final significant digit

What is the stem of 23?

2

What is the leaf of 23?

3

What is the stem of 432?

43

What is the leaf of 432?

2

What is the stem of 5,432?

543

What is the leaf of 5,432?

2

What is the stem of 9.3?

9

What is the leaf of 9.3?

3

How are the stems arranged in a stem-and-leaf plot?

Vertically from smallest to largest

Where are the leaves written in a stem-and-leaf plot?

To the right of their corresponding stem

How should the leaves be arranged in a stem-and-leaf plot?

In increasing order from smallest to largest

What should you look for when reading a stem-and-leaf plot?

The overall pattern, center, spread, and possible outliers

What is one advantage of a stem-and-leaf plot?

It gives a quick visual picture while still showing the exact individual data values

What is an outlier?

A data value that does not fit the general pattern of the rest of the data

What is another name for an outlier?

An extreme value

How does an outlier usually appear on a graph?

It appears separated from or does not fit the main pattern of the data

Why might an outlier occur?

It could be caused by a data-entry mistake or could represent something unusual that actually happened

Why should you investigate an outlier?

Because you need to determine whether it is an error or a meaningful unusual value

What is a line graph used for in statistics?

Displaying specific data values and showing how frequency changes between those values

What is plotted on the x-axis of the line graph described in the textbook?

The data values

What is plotted on the y-axis of the line graph described in the textbook?

Frequency points

How are the points connected on a line graph?

With line segments

What is a bar graph?

A graph that uses separate bars to represent categories or groups of data

How are the bars in a bar graph different from histogram bars?

Bar graph bars are separated by spaces, while histogram bars touch each other

Can bar graphs have horizontal bars?

Yes

Can bar graphs have vertical bars?

Yes

What can the bars in a bar graph represent?

Different categories or groups of data

What is a histogram?

A graph that uses touching bars to show how numerical data are distributed across intervals

What is another word for the intervals in a histogram?

Classes or class intervals

Why are histograms useful for large data sets?

They can display a large number of data values in an easy-to-see visual pattern

When is a histogram commonly recommended?

When a data set has about 100 or more values

How are histogram bars different from bar graph bars?

Histogram bars touch because they represent continuous numerical intervals, while bar graph bars are separated because they represent distinct categories

What does the horizontal axis of a histogram represent?

The numerical variable or intervals into which the data are grouped

What can the vertical axis of a histogram represent?

Frequency, relative frequency, percent frequency, or probability

What does frequency mean?

The number of times a particular value or group of values occurs

What does relative frequency tell you?

The proportion of the total data that falls into a particular group

What is the formula for relative frequency?

RF = f/n

What does f represent in the relative frequency formula?

The frequency of the group or interval

What does n represent in the relative frequency formula?

The total number of data values

How can relative frequency be written as a percentage?

Multiply the relative frequency by 100

If 3 out of 40 students received a certain score range, what is the frequency?

3

If 3 out of 40 students received a certain score range, what is the total number of observations?

40

If 3 out of 40 students received a certain score range, what is the relative frequency?

3/40 = 0.075

If the relative frequency is 0.075, what percentage does it represent?

7.5%

What does a histogram allow you to see about a data set?

The shape, center, and spread of the data

What should you decide first when constructing a histogram?

How many bars or class intervals you want to use

How many classes do many histograms use for clarity?

About 5 to 15 classes

Why should you avoid having too many histogram classes?

Too many bars can make the graph difficult to read and understand

What should the starting point of a histogram be compared with the smallest data value?

It should be slightly less than the smallest data value

What is a convenient starting point for a histogram?

A value slightly below the smallest data value, carried to one more decimal place than the data

Why is the starting point carried to one additional decimal place?

So that data values do not fall exactly on a class boundary

What does greater precision mean when choosing a histogram boundary?

Using more decimal places to make the boundaries more exact

If the smallest value is 60.0 and the data have one decimal place, what convenient starting point can be used?

59.95

Why would 59.95 be used instead of 60 when the smallest value is 60?

It places the boundary slightly below the smallest value and uses one additional decimal place

If the smallest value is 2 and all the data are integers, what convenient starting point can be used?

1.5

Why is 0.5 commonly subtracted from an integer when creating histogram boundaries?

It places the integer values in the middle of the intervals instead of directly on the boundaries

What should the ending point of a histogram be compared with the largest data value?

It should be slightly greater than the largest data value

How can you find the ending point when the data have one decimal place?

Add 0.05 to the largest value