6th Gr. The Statistical Process

Variability

means that the value of the attribute you are studying can change from one person or thing to another.

Statistical process

has four components: STEP 1 Formulate a statistical question. STEP 2 Collect appropriate data. STEP 3 Analyze the data graphically and numerically. STEP 4 Interpret the results of the analysis.

Statistical question

is a question that anticipates an answer based on data that vary.

Data

are categories, numbers, or observations gathered in response to a statistical question.

Categorical data

or qualitative data, fit into exactly one of several different groups or categories.

Quantitative data

is numeric data.

Population

is an entire set of items from which you collect data.

Sample

is a selection from a population.

Survey

is where you ask people one or more questions

Observational study

is where the researcher (you!) collects data by observing the variable of interest.

Experiment

is where the researcher imposes a condition and observes the results.

Bar graph

displays categorical data using either horizontal or vertical bars on a graph. The height or length of each bar indicates the value for that category.

Circle graph

often called a pie chart, displays categorical data using sectors, or "wedges," of a circle. It shows how parts of the whole relate to the whole and how parts of the whole relate to the other parts. The area of each sector corresponds to the ratio of the part in relation to the whole.

Frequency

is the number of times an item or number occurs in a data set.

Mode

is the value or values that occur most frequently in a data set.

Dot plot

is a data display that shows discrete data on a number line with dots, Xs, or other symbols. Dot plots help organize and display a small number of data points.

Distribution

The way the data spreads out.

Symmetric

The peak of the data is in the middle. • The left and right halves of the graph are mirror images, or almost mirror images, of each other.

Skewed right

The peak of the data is to the left side of the graph. • There are only a few data points to the right side of the graph.

Skewed left

The peak of the data is to the right side of the graph. • There are only a few data points to the left side of the graph.

Clusters

areas where data group close together.

Gaps

areas where there are no data.

Peaks

values that contain more data points than the values on either side of it.

Outliers

data values that lie a large distance from the other data. Outliers usually accompany gaps in data.

Uniform distribution

describes the shape of data spread equally across the range of the data set. A uniform distribution appears symmetric but has no distinct peaks.

Stem-and-leaf plot

is a graphical method used to represent ordered numeric data.

Histogram

is a graphical way to display quantitative or numeric data using vertical bars.

Range

is the difference between the maximum and minimum values of a data set.

Grouped frequency table

organizes data according to how many times the data values within a given range of values occur.

Measure of center

tells you how data values cluster, or where the "center" of the data is.

Median

is the middle number in a data set when you place the values in order from least to greatest or greatest to least.

Balance point

When all the points at the same value, you balance the number line with this value.

Mean

is the arithmetic average of the numbers in a data set. You calculate the mean by adding all of the values in the data set and dividing the sum by the number of values.

Quartile

the numbers that split data into quarters (or fourths).

Measure of variation

describes the spread of data values. One measure of variation is the range.

Interquartile Range

is the difference between the third quartile and the first quartile, or Q3 - Q1. The IQR indicates the range of the middle 50 percent of the data.

Box-and-whisker plot

is a graph that displays the five-number summary of a data set. Also known as a box plot.

Deviation

this indicates the distance of a data value from the mean.

Absolute deviation

the absolute value of each deviation.

Mean absolute deviation

is the mean of the absolute deviations.