Chapter 2

frequency

Number of times for each category (simplest)

The numbers used to separate the classes of a frequency​ distribution, but without the gaps created by class​ limits, are called​ ____________________.

class boundaries

stem and leaf display

splits the data values into stems and leaves. by listing all the leaves to the right of each stem, we graphically describe how the data are distributed.

Pie Charts

excellent tool for comparing proportions for categorical data. Each category occupies a segment of the pie that represents the relative frequency of that category

discrete data

- values based on observations that can be counted and are numbers typically represented by whole numbers. - often involved counting observations - because ability to be counted, they have a finite number of values within an interval

Continuous data

- values that can take on any real numbers, including numbers that contain decimal points. - often the result of measuring observations - have infinite number of values available

After constructing any relative frequency​ distribution, what should be the sum of the relative​ frequencies?

1 or 100%

What is wrong with the following class limits for organizing weight data for a sample of 200 adult men in the United​ States? ​140-150 pounds ​150-160 pounds ​160-170 pounds ​170-180 pounds ​180-190 pounds ​190-200 pounds ​200-210 pounds ​210-220 pounds ​220-230 pounds

the classes are overlapping

range

the range of cells from which you are counting

criteria

the value that you are counting

cumulative relative frequency distribution

totals the proportion of observations that are less than or equal to the class at which you are looking. (add relative frequency up to 1.0)

2^k ≥ n

k = number of classes n = number of data points the trick is to find the lowest value of k that satisfies the rule. For example: n = 50 2^5 = 32 ≤ 50 (k=5 too small) 2^6 = 64 ≥ 50 (k=6 good choice)

dependent variable

placed on vertical axis of the scatter plot and is influenced by changes in the independent variable which is placed on the horizontal axis

contingency tables

provide a format to display the frequencies of two qualitative variables - help us identify relationships between two or more variables

scatter plot

provides a picture of the relationship between two quantitative variables that are paired together.

chapter two review page

66

Suppose you want to know if more technical service calls are made to homes with cable television or with satellite dish television. Should you use frequencies or relative frequencies to make the​ comparison? Why?

Relative frequencies should be used since there is likely a difference in the number of users of cable and satellite television. If you make comparisons using​ frequencies, the results can be very misleading for different population sizes.

Which of the statements below is true concerning bar​ graphs?

The height of each bar represents the​ category's frequency or relative frequency.

bar charts

a good tool for displaying qualitative data that have been organized in categories and can be arranged in a vertical or horizontal orientation

histogram

a graph showing the number of observations in each class of a frequency distribution. (similar to bar graph) - when displaying descrete data, their are gaps inbetween bars indicating the frequency of each class continuous data do not have gaps between bars.

line chart

a special type of scatter plot in which the data points in the scatter plot are connected with a line

A frequency distribution lists the​ _________ of occurrences of each category of​ data, while a relative frequency distribution lists the​ _________ of occurrences of each category of data.

number; proportion

The​ ____________________ is the difference between two consecutive lower class limits or two consecutive upper class limits.

class width

relative frequency distributions

display the proportion of observations of each class relative to the total number of observations. (decimal percentage.)

pareto charts

essentially bar charts that show the frequency of the categories that cause quality control problems. The charts show the categories in a decreasing order.

class width formula

estimated class width = (maximum data value - minimum data value) / k ex: (17.4 - 0.6) / 6 = 2.8 (class width)

percentage polygon

graphs the midpoint of each class as a line rather than a column. The height of each midpoint represents the relative frequency of the corresponding class. - more appropriate over histograms when comparing the shape of two or more distributions on one graph

stacked bar chart

group several values in a single column within the same category in a vertical direction

clustered bar charts

group several values side by side within the same category in a vertical direction

​A(n) ____________________ is a bar graph in which the height of each rectangle is the frequency or relative frequency of the class. The width of each rectangle is the​ same, and the rectangles touch each other.

histogram

symmetrical distribution

is one in which the right side of the distribution is the mirror image of the left side of the distribution.

qualitative data

values that are categorical (nominal or ordinal measurement levels) that describe a characteristic, such as gender or level of education.