### MS 150 Statistics fall 2005 quiz 03 • Name:

YearPopulation census¹
18242000
18451690
18561106
1859748
1864600
1874397
1880200
1900500
19371267

The table shows population data for Kosrae in the 1800s and early 1900s. Values before 1856 are estimates and interpolations. Note that here the use of the term "population" refers to the "number of people" on Kosrae and not the term population as used in this class. The counts shown have to be treated as sample data due a lack of knowledge as to the collection techniques employed. The population decline in the 1800s was due to introduced diseases such as influenza as well as sexually transmitted diseases.

1. __________ Find the sample size n for the Kosrae population data.
2. __________ Find the minimum Kosrae population data.
3. __________ Find the maximum Kosrae population data.
4. __________ Find the range of the Kosrae population data.
5. __________ Find the median Kosrae population data.
6. __________ Find the mode for the Kosrae population.
7. __________ Find the sample mean x Kosrae population data.
8. __________ Find the sample standard deviation sx for the Kosrae population data.
9. __________ Find the sample coefficient of variation CV.
10. __________ ≤ 75% of the data ≤ __________ Based on Chebyshev's theorem, calculate the population values that encompass 75% of the data by calculating the mean minus two standard deviations and the mean plus two standard deviations.
Table of statistical functions used by Excel
Statistic or Parameter Symbol Equations Excel
Sample mean x Σx/n =AVERAGE(data)
Sample standard deviation sx =STDEV(data)
Sample Coefficient of Variation CV sx/x =STDEV(data)/AVERAGE(data)
Chebyshev's Theorem: The proportion of the data that must lie within k standard deviations on either side of the mean is at least: - 1-(1/k²)

¹ The 2000 number for 1824 is attributed by Wilson to Duperrey, the missionaries would later estimate the pre-contact population at 5000.