5-Minute Check on Activity 7-4. Given the following data: 8, 1, 9, 2, 3, 4, 4, 5, 5, 6, 7, 8, 8 Find the mean Find the median Find the mid-range Find the mode What are the four descriptors of a distribution? What are the three types of shape? Which measures of center are resistant?.
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5-Minute Check on Activity 7-4
Sum=70 70 / 13 = 5.38
Middle value of 13 is the 7th: 5
(min+max)/2 = (1 + 9) / 2 = 5
8 occurs the most often
Shape, Outliers, Center, Spread
Skewed left, symmetric, skewed right
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Activity 7 - 5
Sampling a Population
Suppose you have a need to know the average weight of adults in the United States, or the mean age of blue crabs in the Chesapeake Bay, or the median household income in the Commonwealth of Virginia. To determine such measures of central tendency, it is not usually practical to obtain the data for every individual in the population.
Why is it not possible to conduct a census on the populations described above?
US adults - costly as the census is done only every 10 years and still misses people
Blue crabs - we would have to empty the Bay to get them all
Household income - similar to the census; plus people don’t tell you the truth always about how much money they make
Since a sample can be of any size, how would you compare the practicality and usefulness of samples of size 1, 25, 2000, and 2 million when attempting to estimate the mean household income in Virginia.
Size n=1 easy to do, but what does it really show?
Size n=25 still easy to do, and it shows more data so it would be more significant
Size n=1 harder to do, but the results would be even more significant
Size n=1 very hard to do – nearing census like, but the results be have the strongest significance
Larger samples are better and more accurate, but there are always trade-offs in time and money.
Exact samples needed to get a certain accuracy can be determined by a mathematical formula (beyond our course). These numbers are most often seen in surveys reported in the media (with accuracy listed as percentage points).
Non sampling Error
sample gives incomplete information about the population
Data-entry (input) errors
The table below shows the current grades for all 20 students in Mr. Horton’s economics class.
Use randint(lower bound, upper bound, # needed)
Mean = 79 and Median = 79.5 (??)
Population values; for mean,
4, 17, 8, 1, 7, 6, 5, 7, 19, 20
95, 62, 65 mean = 74 median = 65
18, 5, 16, 4, 1, 10, 20, 18, 2, 9
88, 71, 79, 95, 78 mean = 82.2 median = 79
11, 11, 15, 3, 10, 2, 1, 17, 1, 10, 17, 15, 18, 10, 20 3, 19, 13, ….
67, 81, 82, 78, 84, 78, 62, 88, 63, 93 mean = 77.6 median = 79.5
just get some more and keep eliminating numbers already chosen
The sample values should approach the population values
We started off with the same seed value and the calculator produces pseudorandom numbers (see www.random.org)