Learn: Statistics and Data Analysis

What is discrete data?

Data that can be counted. It usually uses separate/countable values.

What is continuous data?

Data that can take any value within a range, including decimals.

What is an example of discrete data?

The number of students in a room.

What is an example of continuous data?

Height, weight, volume, or time.

What is the easiest way to remember discrete vs. continuous?

Discrete = COUNT. Continuous = MEASURE.

What is a histogram?

A graph showing numerical data grouped into intervals called bins.

What are bins?

Intervals used to group numerical data in a histogram.

What does the horizontal axis of a histogram show?

The values or intervals of the numerical variable.

What does the vertical axis of a histogram show?

The count or percentage of observations.

What is a stem-and-leaf plot?

A display that organizes numerical data into stems and leaves while keeping the individual values visible.

What is another name for a stem-and-leaf plot?

A stemplot.

What is a stem-and-leaf plot similar to?

A histogram turned sideways.

How do you make a stem-and-leaf plot?

Divide each value into a stem and leaf, list all possible stems, place each leaf on its stem, and sort the leaves in ascending order.

In a stem-and-leaf plot, how are the leaves organized?

From 0 through 9 in ascending order.

In the class example, what does 0 | 2 represent when the leaf is the tenths digit?

0.2.

What does 17 | 2 represent when the leaf is the tenths digit?

17.2.

What is a bar graph used for?

Showing frequencies or percentages for categories.

What is a pie chart useful for?

Comparing each category as a part of the whole.

What is a boxplot?

A graph that summarizes numerical data using quartiles and the median and can show outliers.

What does a boxplot help show?

The center, spread, quartiles, and possible outliers.

What should you look for when examining a distribution?

Center, spread, shape, and outliers.

What is a symmetric distribution?

A distribution where the left and right sides are approximately mirror images.

What is a skewed distribution?

A distribution where one tail is longer than the other.

What is a right-skewed distribution?

A distribution whose long tail extends to the right.

What is a left-skewed distribution?

A distribution whose long tail extends to the left.

How do you determine whether a distribution is right-skewed or left-skewed?

Look at the direction of the long tail.

If the long tail points right, what is the distribution?

Right-skewed.

If the long tail points left, what is the distribution?

Left-skewed.

What is a bimodal distribution?

A distribution with two distinct peaks.

What does "bi" in bimodal mean?

Two.

What is an outlier?

An observation that noticeably departs from the general pattern of the data.

What are the three measures of central tendency?

Mean, median, and mode.

What is the mean?

The average of the data.

How do you calculate the mean?

Add all the values and divide by the number of values.

What is the median?

The middle value when the data is arranged from smallest to largest.

What do you do if there are two middle values?

Average the two middle values.

What is the mode?

The value that occurs most frequently.

Can a dataset have more than one mode?

Yes.

Can a dataset have no mode?

Yes.

What is an easy way to remember mean, median, and mode?

Mean = Average. Median = Middle. Mode = Most.

What does variability describe?

How spread out or varied the data is.

What are the three measures of variability?

Range, interquartile range (IQR), and standard deviation.

What is the range?

The maximum value minus the minimum value.

What is the formula for range?

Range = Maximum − Minimum.

What is the IQR?

The interquartile range; it measures the spread of the middle 50% of the data.

What does IQR stand for?

Interquartile Range.

What is the formula for IQR?

IQR = Q3 − Q1.

What is Q1?

The first quartile, approximately the 25th percentile.

What is Q3?

The third quartile, approximately the 75th percentile.

What percentage of the data does the IQR represent?

The middle 50%.

What does standard deviation measure?

How spread out the observations are around the mean.

What does a small standard deviation mean?

The observations are relatively close to the mean.

What does a large standard deviation mean?

The observations are more spread out from the mean.

Which measure of variability uses the maximum and minimum?

Range.

Which measure of variability measures the middle 50%?

IQR.

Which measure of variability measures spread around the mean?

Standard deviation.

What happens to variability when data becomes more spread out?

Variability increases.

What is the difference between a histogram and a bar graph?

A histogram displays numerical data grouped into intervals, while a bar graph compares categories.

Is the number of students in a room discrete or continuous?

Discrete.

Why is the number of students in a room discrete?

Because students can be counted and you cannot have a fraction of a student.

Is volume discrete or continuous?

Continuous.

Is height discrete or continuous?

Continuous.

Is time discrete or continuous?

Continuous.

Why can continuous data have decimals?

Because continuous measurements can be divided into increasingly smaller values.

How do you convert a percentage to a decimal?

Move the decimal point two places to the left.

Convert 14.1% to a decimal.

0.141.

Convert 20.8% to a decimal.

0.208.

Convert 29.5% to a decimal.

0.295.

Convert 35.6% to a decimal.

0.356.

Data: 2, 4, 6, 8, 10. What is the mean?

6.

Data: 2, 4, 6, 8, 10. What is the median?

6.

Data: 2, 4, 6, 6, 10. What is the mode?

6.

Data: 2, 4, 6, 8, 10. What is the range?

8.

If a distribution has two peaks, what is it?

Bimodal.

If a distribution has a long tail pointing right, what is it?

Right-skewed.

If a distribution has a long tail pointing left, what is it?

Left-skewed.

If both sides of a distribution are approximately mirror images, what is it?

Symmetric.

If one observation is unusually far away from the rest, what is it?

An outlier.

Mean means what?

Average.

Median means what?

Middle.

Mode means what?

Most frequent.

Range means what?

Maximum minus minimum.

IQR means what?

Q3 minus Q1, representing the middle 50%.

Standard deviation means what?

The spread of observations around the mean.

Histogram means what?

Numerical data grouped into intervals.

Bar graph means what?

Categories.

Boxplot means what?

A display using quartiles and the median that can also show outliers.

Stem-and-leaf plot means what?

A display that organizes numerical data while keeping the individual values visible.