Chapter 2: Graphical Descriptions of Data Flashcards
distribution
a way to describe the structure of a particular data set or population
frequency distribution
a display of the values that occur in a data set and how often each value, or range of values, occurs
frequencies (f)
the numbers of data values in the categories of a frequency distribution
class
a category of data in a frequency distribution
class width
the difference between the lower limits or upper limits of two consecutive classes of a frequency distribution
class width = (highest value - lowest value) ÷ number of classes
lower class limit
- the smallest number that can belong to a particular class
- same number of decimal places as the largest number of decimal places in the data
upper class limit
- the largest number that can belong to a particular class
- same number of decimal places as the largest number of decimal places in the data
class boundary
- the value halfway between the upper limit of one class and the lower limit of the next class
class boundary = (Class 1 upper limit + Class 2 lower limit) ÷ 2
- After finding one class boundary, add or subtract the class width to find the next class boundary. The boundaries of a class are typically given in interval form: lower boundary–upper boundary
midpoint (class mark)
(lower limit + upper limit) ÷ 2
relative frequency
relative frequency = f ÷ n
sample size
n = Σfi
cumulative frequency
- the sum of the frequencies of a given class and all previous classes
- the cumulative frequency of the last class equals the sample size (Σfi)
pie chart
- shows how large each category is in relation to the whole
- round each angle measure to the nearest whole degree
- qualitative data
bar graph
- bars represent the amount of data in each category
- one axis displays categories, and the other displays frequencies
- qualitative data
Pareto chart
- bar graph in descending order
- typically used with nominal data
- qualitative data
side-by-side bar graph
- a bar graph that compares the same categories for different groups
- qualitative data
stacked bar graph
- bar graph that compares the same categories for different groups and shows category totals
- qualitative data
histogram
- a bar graph of a frequency distribution of quantitative data
- horizontal axis is a number line
- quantitative data
relative frequency histogram
- a histogram in which the heights of the bars represent the relative frequencies of each class rather than simply the frequencies
- quantitative data
frequency polygon
- visual display of the frequency of each class of quantitative data that uses straight lines to connect points plotted above the class midpoints
- quantitative data
ogive
- shows the cumulative frequency of each class, created by adding a 0 for the first data point and joining the points together with line segments
- quantitative data
stem-and-leaf plot
- retains the original data
- the leaves are the last significant digit in each data value and the stems are the remaining digits
- requires a key
- quantitative data
dot plot
- displays the data without grouping; only data that are exactly the same appear together
- retains the original data by plotting a dot above each data value on a number line
- quantitative data
line graph
uses straight lines to connect points plotted at the value of each measurement above the time it was taken
required labels on a graph
- title: what it’s about
- axes: categories and data boundaries/classes
- source: where the data came from
time-series graph
used to display a variable whose values change over time
cross-sectional graph
graph that displays information gathered at a single point in time
pictograph
bar graph that uses pictures of objects instead of bars
important aspects of graphs
- appropriateness (type of graph)
- scaling
- shape
- uniform
- symmetric
- skewed to the right
- skewed to the left
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uniform graph
the frequency of each class is relatively the same
symmetric
the data lie evenly on both sides of the distribution
skewed to the right
when the majority of the data fall on the left side of the distribution; the “tail” of the distribution is on the right
skewed to the left
when the majority of the data fall on the right side of the distribution; the “tail” is on the left
outlier
a data value that falls outside the shape of the distribution
