Displaying Distributions with Graphs

the science of collecting, analyzing, and drawing conclusions from data

Descriptive Inferential

the methods of organizing & summarizing data

involves making generalizations from a sample to a population

the entire collection of individuals or objects about which information is desired

a subset of the population, selected for study in some prescribed manner

any characteristic whose value may change from one individual to another

observations on single variable or simultaneously on two or more variables

Who? What? Why?

What individuals do the data describe? How many individuals appear in the data?

How many variables? What are the definitions of these variables? What units?

What is the reason data were gathered?

Also called “qualitative” Identify basic differentiating characteristics of the population

Also called “numerical” Observations or measurements that take on numerical values Makes sense to average these values Two types-discrete & continuous

Listable set of values Usually counts of items

Data can take on any value in the domain of the variable Usually measurements of something

Univariate-data that describes a single characteristic of the population Bivariate-data that describes two characteristics of the population Multivariate-data that describes more than two characteristics

Which category of variables would the following be? Gender Age Hair color Smoker Systolic blood pressure Number of girls in class

4 Common Types

Tells us what values the variable takes and how often it takes these values One variable may take values that are very close together while others might be spread out

Refers to data in which both sides are (more or less) the same when the graph is folded vertically down the middle Bell-shaped is a special type Has a center mound with sloping tails

Refers to data in which every class has equal or approximately equal frequency

Refers to data in which one side (tail) is longer than the other side The direction of the skewness is on the side of the longer tail Skewed rightSkewed left

Refers to data in which two or more classes have the largest frequency and are separated by at least one other class

Normal, Symmetrical Skewed Uniform Bimodal

Where the middle of the data falls 3 types of central tendency Mean, median, mode

Shows how spread out the data is Refers to the variability of the data Range, standard deviation, IQR

Outliers-value that lies away from the rest of the data Clusters Gaps

1. Bar 2. Pie Chart 3. Dotplot 4. Stem-and-Leaf 5. Histogram 6. Relative cumulative frequency graph 7. Time Plot 8. Box & Whisker 9. Scatter

Must label the axes and title the graph Scale your axes Draw vertical bar above each category name to a height that corresponds to the count in that category

The graph below shows the proportion of the female labor force aged 25 and older in the United States that falls into various educational categories. The coding used in the plot is as follows: 1. none-8 th Grade6. bachelor’s degree 2. 9 th grade-11 th grade7. master’s degree 3. high school graduated8. professional degree 4. some college, no degree9. doctorate degree 5. associate degree Proportion Educational Attainment (women)

Must include all categories that make up a whole.

Tally marks are made for each set of data. The data below is graphed on the dotplot on the right

A stem and leaf plot displays data like a bar graph, but we break the data apart into stem and leaf plots. The data point 30 is broken up into 3 0 stem leaf The data point for 304 is broken up into 30 4 stem leaf

The data set {30, 27, 34, 28, 45, 31, 34, 40, 29} is represented by: 2: : : 0 5 The 2 and 9 represents the data point 29. The stems are the tens place and the leaves are the ones digits. Notice numbers are listed in order from smallest to largest.

Draw a bar graph that represents the count in each class. Leave no horizontal space (unlike a bar graph). The data below is graphed on the dotplot on the next slide

Also called an Ogive. A relative frequency histogram has the same shape and the same horizontal scale as the corresponding frequency histogram. The difference is that the vertical scale measures the relative frequencies (measured as a percentage), not frequencies.

The frequency needs to be changed to percentages.

Place the time on the x axis. Time is the explanatory variable. Place the observations on the y axis. The observations represent the response variable.

These will be discussed later. Box and Whisker-Section 1.2 Scatter Plot-Section 3.1

The distribution of a variable tells us what values it takes and how often it takes these values. To describe a distribution, begin with a graph. Bar graphs and pie charts display the distributions of categorical variables. These graphs use the counts or percents of the categories. Stem & Leaf plots and histograms display the distributions of qualitative variables. Stem & Leaf Plots separate each observation into a stem and a one-digit leaf. Histograms plot the frequencies (counts) or percents of equal-width classes of values.

When examining a distribution, look for the shape, center and spread, and for clear deviations from the overall shape. Some distributions have simple shapes, such as symmetric or skewed. Others may be bimodal (more than one major peak). Outliers are observations that lie outside the overall pattern of a distribution. Always look for outliers and try to explain them.

A relative frequency graph (ogive) is a good way to see the relative standing of an observation. When observations on a variable are taken over time, make a time plot that graphs horizontally and the values of the variable vertically. A time plot can reveal trends (patterns) or other changes over time.

On page 64 in your textbook, complete exercises 1.13 and 1.16.