BSTAT module 3

raw data

When data is collected from a survey or designed experiment, they must be organized into a manageable form. Data that is not organized is referred to as ________

tables, graphs, numerical summaries

Ways to Organize Data

frequency distribution

lists each category of data and the number of occurrences for each category of data.

relative frequency

is the proportion (or percent) of observations within a category and is found using the formula:

relative frequency distribution

lists the relative frequency of each category of data

bar graph

is constructed by labeling each category of data on either the horizontal or vertical axis and the frequency or relative frequency of the category on the other axis

bar graph

A rectangle of equal width is drawn for each category whose height is equal to the category's frequency or relative frequency

pareto chart

is a bar graph where the bars are drawn in decreasing order of frequency or relative frequency

Pie chart

is a circle divided into sectors.

Each sector represents a category of data. The area of each sector is proportional to the frequency of the category

lower class limit

identifies the smallest possible data value assigned to the class

upper class limit

identifies the largest possible data value assigned to the class

class boundaries

the true or real limits of an interval

class boundaries

the specific points that serve to separate adjoining classes along a measurement scale for continuous variables

class boundaries

can be determined by identifying the points that are halfway between the upper and lower stated class limits, respectively, of adjoining classes

class marks/midpoints

the value halfway between the lower and upper class limits

relative frequency

obtained by dividing the class frequency by the total frequency

percentages

obtained by multiplying the relative frequencies by 100%

cumulative frequencies

the number of data items with values less than or equal to the upper class limit of each class; obtained by summing the frequencies

cumulative percentages

obtained by dividing the cumulative frequencies by the total number of cases and then multiplying the result by 100.

cumulative percentages

provide information on the percentage of values less than or equal to a specified value.

histogram

A graph consisting of a series of vertical columns or rectangles with no gaps between bars.

each bar is drawn with a base equal to the class boundaries and a height corresponding to the class frequency

histogram

a suitable graph for representing data obtained from continuous variables

frequency polygon

Constructed by plotting class marks (X) against class frequencies (Y) and connecting the consecutive points by straight lines

to close the frequency polygon, an additional class interval is added to both ends of the distribution, each with zero frequency

ogive

A graph of a cumulative frequency distribution plotting the upper class boundaries (X) against the cumulative frequencies (Y)

the lower end of the graph is connected to the X-axis by adding another interval

Ogive

Used to visually represent how many values are below a specified upper class boundary

stem and leaf plot

a type of graph that is similar to a histogram

but shows more information.

• summarizes the shape of a set of data (the distribution) and provides extra detail regarding individual values.

• the data are arranged by place value:

Stems - the digits in the largest place

Leaves - the digits in the smallest place

Summarizes quantitative data.

• Each data point is broken down into a “stem” and a “leaf.”

• First, “stems” are aligned in a column.

• Then, “leaves” are attached to the stems

uniform distribution

One way to describe the shape of a distribution is by its number of peaks, or modes

uniform distribution

has no mode because all data values have the same frequency.

symmetric distribution

the shape of the left side of the distribution is a mirror image of the right side

● its left half is a mirror image of its right half

normal distribution

symmetric distribution with a single peak and a bell shape is known as a ______

normal distribution

When the overall pattern of a large number of observations is so regular, we can describe it as a smooth curve

normal curves

are symmetric and bell-shaped, smoothed-out histograms.

symmetric distribution

mean = median = mode

skewed

the two sides of the distribution are not mirror images of each other

right skewed or positively skewed if

the values are more spread out on the right. It has a tail pulled toward the right.

For positively skewed distributions:

mean > median

left- skewed or negatively skewed

if the values are more spread out on the left, meaning that some low values are likely to be outliers.

For negatively skewed distributions:

mean < median