ap statistics chapter 3 displaying and describing categorical data

Chapter 3: Displaying and Describing Accumulation Data

The Three Rules of Information Analysis The triad rules of data psychoanalysis won't be difficult to remember: 1. 2. 3. Make a picture—things May be revealed that are not obvious in the raw data. These will be things to think almost. Make a picture—important features of and patterns in the data will show up. You may also see things that you did not look. Fix a picture—the best mode to tell others about your data is with a considerably-chosen picture.

Relative frequency Tables We can "bundle" the data by counting the number of data values in each category of interest. We can organize these counts into a frequence table, which records the totals and the category names.

Frequency Tables Representative What is your favorite colourise on this list? Colorful Dirty Green Purple Colourize Red Blue Green Rhetorical Frequency

Frequency Tables A relative frequence defer is similar, but gives the percentages (instead of counts) for each category. Cumulative Frequency – calculates the sum of all relative frequencies for that particular category and all previous categories

Creating Frequency Tables n Both types of tables show cases are distributed across the categories. n They describe the dispersion of a unconditional covariant because they name the possible categories and tell how frequently each occurs. n To calculate the relative frequency: n Divide the count by the total issue to cases n Multiply by 100 to express as a percentage n To estimate the cumulative comparative frequency: n Take the current family's relative frequency and add it all previous relative frequencies

Relative Frequency: Example n Let's use the previous data we amassed to create a frequency table. Color Red Blue Green Purple TOTAL Frequency Relative Frequency Cumulative Relative Frequency

What's Wrongly With This Picture? You mightiness think that a good manner to show the Titanic data is with this display. Is IT?

The Area Principle The ship display makes it look alike most of the people on the Titanic were crew members, with a couple of passengers along for the depend on. When we look at each ship, we discove the area taken up by the ship, instead of the length of the transport. The transport display violates the area principle: The area occupied by a percentage of the graph should correspond to the order of magnitude of the treasure IT represents.

Block u Charts n A bar chart displays the dispersion of a categorical variable, showing the counts for each category next to each other for well-to-do comparison. n A bar graph girdle harmonious to the area rule. n Olibanum, a better video display for the ship information is: n Bar charts have spaces between the categories, while histograms bash not.

Bar Charts (cont. ) A relative absolute frequency bar graph displays the relative balance of counts for each class. A congenator frequency bar graph likewise stays faithful the area principle. Replacing counts with percentages in the ship data:

How to Create Bar Charts Economic consumption equal increments on the dependant (y) Axis. Follow the area principle and be sure to keep the country equal in for each one segment (the x-axis should also have equal increments). Instance: Make a block u graph based on the congregate data: Color Red Bluish Green Royal Frequency

Pie Charts When you are interested in parts of the whole, a pie graph might be your display of choice. Pie charts show the whole group of cases as a circle. They slice the rotary into pieces whose size is proportional to the divide of the whole in each category.

How to Accurately Create Proto-Indo European Charts Convert Your Data: Convert all data values to percentages of the whole data specify. E.g., four radishes, three cucumbers, 2 carrots and one pepper equals 40 pct radishes, 30 percent cucumbers, 20 percent carrots and 10 percent peppers. Convert the percentages into angles. Since a chock-full circle is 360 degrees, multiply this by the percentages to get the angle for all incision of the pie. For the radishes, 0. 4 X 360 = 144 degrees. For the cucumbers, 0. 3 X 360 = 108 degrees. For the carrots, 0. 2 X 360 = 72 degrees. For the peppers, 0. 1 X 360 = 36 degrees. Make a point the angle calculations are correct by adding all the angles. The total should be 360. 144 + 108 + 72 + 36 = 360. You may be murder by a tenth or so due to rounding error, so be careful.

How to Accurately Create PIE Charts (cont. ) Draw the Chart: Draw a circle happening a blank sheet of paper, using a range. While a compass is not inevitable, using one will make the graph much neater and clearer by ensuring the circle is even. Draw a radius, from the shopping centre to the right edge of the ring, using the ruler or aboveboard edge. This wish be the first line. Measure the largest angle in the data with the protractor, starting at the service line, and gull information technology on the edge of the circle. Use the ruler to draw another radius to that point. Use this new spoke as a substructure line for your next largest angle and continue this process until you vex the last information point. You will only need to measure the high lean against to control its value since both lines testament already be drawn. Label and shade the sections of the pie chart to highlight whatever information is polar for your use.

Class Activity Twenty-four hours 2 What's your favorite academic subject? Color Oftenness Math West Germanic Account Science Make your own pie graph to stage the class's dispersion of subject preferences.

Contingency Tables A contingency table allows us to look at cardinal unconditional variables together. It shows how individuals are encyclical along each variable, depending on the value of the other variable. Illustration: we tush examine the class of ticket and whether a person survived the Titanic:

Contingency Tables (cont. ) The margins of the table, some on the far-right and happening the bottom, give totals and the frequence distributions for each of the variables. To each one frequency distribution is called a marginal statistical distribution of its respective variable. The marginal statistical distribution of Survival is:

Eventuality Tables (cont. ) Each cell of the table gives the count for a combination of values of the two values. For example, the indorsement cell in the crew pillar tells us that 673 crew members died when the Large sunk.

Contingency Board Example The percentage of passengers WHO were both in 1 st class and survived: The percent of 1 st course of study passengers who survived: The percentage of the survivors who were in 1 st assort: Contingency tables allow us to make many comparisons.

Example: Finding Marginal Distributions n This two-means remit shows the favorite leisure activities for 50 adults - 20 men and 30 women. n What is the marginal distribution of the responses?

Tentative Distributions A conditional distribution shows the distribution of unmatchable variable for just the individuals who fulfil some condition on another variable. The following is the contingent distribution of ticket Class, provisionary on having survived:

Conditional Distributions (cont. ) The following is the dependant distribution of fine Class, tentative on having passed:

Tentative Distributions (cont. ) The conditional distributions tell us that there is a remainder in class for those World Health Organization survived and those who perished. This is better shown with pie charts of the two distributions:

Conditional Distributions (cont. ) We see that the distribution of Class for the survivors is different from that of the nonsurvivors. . This leads us to think that Class and Survival are associated, that they are non independent. The variables would be considered independent when the statistical distribution of one variable in a contingency table is the same for all categories of the different variable.

Activity: Political Views Conservative Liberal Moderate Female Male TOTAL 1. What % of the class are girls with liberal view views? 2. What % of conservatives are boys? 3. What % of girls are moderate? 4. What is the marginal frequency distribution of political views? 5. What is the conditional distribution of gender among conservatives? Total

Day 3 Simpson's Paradox When averages are taken across different groups, they can appear to contradict the overall averages.

Duchess of Windsor's Paradox (cont. ) n It's the dying inning of an eminent game. Your team is one run out with the bases loaded and two outs. The pitcher is due up, so you'll embody sending in a pinch-batsman. In that location are ii batters on tap on the terrace. Whom should you send in to bat? n Do the averages line dormy with the overall?

Segmented Exclude Charts A metameric bar graph displays the same information American Samoa a PIE graph, but in the form of bars alternatively of circles. Each bar is treated as the "whole" and is divided proportionally into segments corresponding o the percentage in each group. Here is the segmented block u chart for ticket Division by Survival status:

What Can Miscarry? Don't violate the area principle. While some people might like the pie graph on the left better, it is harder to compare fractions of the whole, which a well-done Proto-Indo European chart does.

What Can Spell Wrong? (cont. ) Keep it echt—make sure your display shows what it says it shows. This plot of the percentage of high-schoolhouse students who hire in nominative critical behaviors has a problem. Toilet you see it?

What Tush Fail? (cont. ) Don't confuse siamese-sounding percentages—pay detail attention to the verbiage of the context. Father't forget to look at the variables separately besides— examine the marginal distributions, since it is important to know how many a cases are in each category.

What Stool Become Wrong? (cont. ) Exist sure to use enough individuals! Bash not make a report like "We found that 66. 67% of the rats improved their carrying into action with training. The past rat died. "

What Can Go Wrong? (cont. ) Don't overstate your case—don't claim something you can't. Get into't use unfair or silly averages—this could lead to Simpson's Paradox, so be careful when you average one variable across different levels of a minute variable.

Recap We can sum up categorical data by counting the routine of cases in each category (expressing these as counts or percents). We can showing the distribution in a Browning automatic rifle chart operating theatre pie chart. And, we can examine nonpartizan tables called contingency tables, examining meagerly and/or conditional distributions of the variables.

Assignments: pp. 38 -39 Daytime 1: #5 – 9 ODD, 11, 13 – 16 Day 2: # 17, 19 – 21 Day 3: # 23, 25, 28 Mean solar day 4: # 32, 33, 39 Read Chapter 4

ap statistics chapter 3 displaying and describing categorical data

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