Elementary Statistics: A Step By Step Approach

10th Edition

ISBN: 9781260042054

Author: Bluman

Publisher: MCG

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Textbook Question

Chapter 3.1, Problem 39EC

Median for Grouped Data An approximate median can be found for data that have been grouped into a frequency distribution. First it is necessary to find the median class. This is the class that contains the median value. That is the n/2 data value. Then it is assumed that

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the data values are evenly distributed throughout the median class. The formula is

M D = n 2 − c f f ( w ) + L m

where n = sum of frequencies

cf = cumulative frequency of class immediately preceding the median class

w = width of median class

f = frequency of median class

L_m = lower boundary of median class

Using this formula, find the median for data in the frequency distribution of Exercise 16.

16. Percentage of Foreign-Born People The percentage of foreign-born population for each of the 50 states is represented here. Find the mean and modal class for the data. Do you think the mean is the best average for this set of data? Explain.

Percentage	Frequency
0.8–4.4	26
4.5–8.1	11
8.2–11.8	4
11.9–15.5	5
15.6–19.2	2
19.3–22.9	1
23.0–26.6	1

Source: World Almanac.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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Chapter 3.1, Problem 38EC

Chapter 3.2, Problem 1AC

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Elementary Statistics: A Step By Step Approach

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