Unit 4: Exploring Data

Mosaic Plots

Mosaic Plots

________: Stacked bar chart that shows percentages of data in groups.

Box plots

________: a graph that gives a quick picture of the middle 50 % of the data.

Outliers

________: An observation that is surprisingly different from the rest of the data.

Bivariate data

________: Taking two measurements on each object (Ex.

Dotplot

________: Best for small data sets, similar to histograms and bar plots.

Numerical

________ or Qualitative: Outcomes can be measured arithmetically.

Sample

________: The part of the population that is actually studied.

Quartiles

________: Divide a set of values into four equal parts by using the 25th, 50th, and 75th.

Q1

________: 25 % of values are below and 75 % of values are above.

Correlation Coefficient

________: Numerical measures used to judge the relation between two variables.

standard deviation

Can be qualified through the range, ________, or variance of a distribution.

Q2

________: 50 % of the values are below and 50 % of the values are above.

Spread

________: Describes how far the data points are from the center.

Univariate data

________: Taking only one measurement on each object (Ex.

Histogram

________: a graphical representation in the x- y form of the distribution of data in a data set; x represents the data and y represents the frequency or relative frequency.

Shape

________: Distribution can tell us where most of the data is.

Categorical

________ or Qualitative: Places the individual being studied into one of several groups.

Error

________ or residual= e= y- ŷ= observed values of Y for a given value of X- predicted value of Y for a given value of X.

Population

________: The entire group of individuals or things that we are interested in.

Range

________: The difference between the largest and the smallest measurement in a data set.

graph

The ________ consists of contiguous rectangles.

Scatterplot

________: Graphical summary measure.

Linear regression mode

________: Is an equation that gives a straight- line relationship between two variables.

Direction

________: The scatterplot will show whether the y- value increases or decreases as the x increases, or that it changes ________.

Positive z score

________: Indicates that the measurement is larger than the mean.

Linear Regression

________: If two different qualitative variables have a linear relation, then we can measure the strength of that relationship using this.

Statistics

________: The science of data.

Stem

________- and- leaf graph or stemplot: easy to compute the median and other quantiles.

Positive relation

________: Increasing or upward trend between two variables.

Tabular Methods

________: Frequency distribution table (it facilitates the analysis of patterns of variation among observed data)

regression line

Predicted value: computed using the estimated ________ and is also known as "y hat.

Coefficient of determination

________: measures the percent of the variation in Y- values explained by the linear relation between X- and Y- values.

Descriptive methods

________: The different methods used collect data.

Population mean

________: Adding up all the values in the entire population and dividing by the number of values.

Frequency

________** (f): Number of times that observation has occurred.

Bar Charts

________: The length of the bar for each category is proportional to the number or percent of individuals in each category.

Cumulative Frequency Charts

________: Frequency for that group plus the frequencies of all groups of small observations.

Statistics

The science of data

Descriptive methods

The different methods used collect data

Categorical or Qualitative

Places the individual being studied into one of several groups

Numerical or Qualitative

Outcomes can be measured arithmetically

Univariate data

Taking only one measurement on each object (Ex

Bivariate data

Taking two measurements on each object (Ex

Tabular Methods

Frequency distribution table (it facilitates the analysis of patterns of variation among observed data)

n

Denotes the number of observations

**Frequency (**f)

Number of times that observation has occurred

Relative frequency

Ratio of the frequency to the total number of observations

Cumulative frequency

Gives the number of observations less than or equal to a specific value

Frequency distribution table

A table giving all possible values of a variable and their frequencies

Bar Charts

The length of the bar for each category is proportional to the number or percent of individuals in each category

Pie Chart

Categories of data are represented by wedges in a circle and are proportional in size to the percentage of individuals in each category

Segmented Bar Chart

Takes the distribution from each group and arranges them along either the horizontal or vertical axis and shows the relative frequency of each group represented in one bar for each group

Mosaic Plots

Stacked bar chart that shows percentages of data in groups

Center

Describes the "typical" or central data points

Spread

Describes how far the data points are from the center

Shape

Distribution can tell us where most of the data is

Symmetrical Distribution

The data is spread out in the same way on both sides and there is the same amount of data on each side of the center

Skewed Distribution

If there is an extreme value in only one direction that causes one side to have a longer tail

Cluster sample

A sample in which the researcher first divides the population into sections (or clusters), and then randomly selects all members from some of those clusters

Outliers

An observation that is surprisingly different from the rest of the data

Stem-and-leaf graph or stemplot

easy to compute the median and other quantiles

Dotplot

Best for small data sets, similar to histograms and bar plots

Histogram

a graphical representation in the x-y form of the distribution of data in a data set; x represents the data and y represents the frequency or relative frequency

Cumulative Frequency Charts

Frequency for that group plus the frequencies of all groups of small observations

Population

The entire group of individuals or things that we are interested in

Sample

The part of the population that is actually studied

Mean

The arithmetic means AKA average

Population mean

Adding up all the values in the entire population and dividing by the number of values

Median

Point that divides the measurements in half

Range

The difference between the largest and the smallest measurement in a data set

Interquartile range

The range of the middle 50% of the data, the difference between the third quartile and the first quartile

Standard deviation

A number that is equal to the square root of the variance and measures how far data values are from their mean

Variance

Average of the squares of the deviation

Percentiles

Percentiles divide a set of values into 100 equal parts

Quartiles

Divide a set of values into four equal parts by using the 25th, 50th, and 75th

Q1

25% of values are below and 75% of values are above

Q2

50% of the values are below and 50% of the values are above

Q3

75% of values are below and 25% of values are above

Standardized scores or z-scores

Gives the distance between the measurements and the mean in terms of the number of standard deviations

Negative z-score

Indicated that the measurements are smaller than the mean

Positive z-score

Indicates that the measurement is larger than the mean

Box plots

a graph that gives a quick picture of the middle 50% of the data

Bivariate data

Data on two different variables collected from each item in a study

Linear Regression

If two different qualitative variables have a linear relation, then we can measure the strength of that relationship using this

Scatterplot

Graphical summary measure

Shape

A scatter plot tells us whether the nature of the relation between the two variables in linear or nonlinear

Direction

The scatterplot will show whether the y-value increases or decreases as the x increases, or that it changes direction

Positive relation

Increasing or upward trend between two variables

Negative relation

Decreasing or downward trend between the two variables

Strength of relationship

If the trend of the data can be described with a line of the curve then the spread of the data values around the line or curve describes the degree of the relation between the two

Correlation Coefficient

Numerical measures used to judge the relation between two variables

Linear regression mode

Is an equation that gives a straight-line relationship between two variables

Independent variable

x

Dependent variable

y

Slope

b

y-intercept

a

Predicted value

computed using the estimated regression line and is also known as "y hat"

Least square regression line

line that minimizes the sum of the squares of the residuals

Outliers

are observed data points that are far from the least squares line

Influential points

observed data points that are far from the other observed data points in the horizontal direction