Answered: Compute the mode, median, and mean for…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 4BGP

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Question

The following table lists the Democratic vote percentages for House elec-
tions in ten state districts before and after the Supreme Court forced states
to reapportion districts to guarantee equal populations in each. Compute
the mode, median, and mean for each list (all ten districts). Interpret and
compare the figures for each list (1964 vs. 1966). Note: this is a list, not a
frequency distribution—the unit of analysis is a congressional district, the
number of cases = 10.

D1 56 62
D2 65 62
D3 57 58
D4 72 67
D5 71 64
D6 67 62
D7 35 41
D8 45 48
D9 62 68
D10 48 49

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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