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

$MD=\frac{\frac{n}{2}-cf}{f}(w)+L_m$

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.