Chapter 3.2
A random sample of 10 subjects have weights with a standard deviation of 9.9564kg. What is the variance of their weights? Be sure to include the appropriate units with the result
The variance of the sample data is 99.1299kg2
Listed below are prices in dollars for one night at different hotels in a certain region. Find the range, variance, and standard deviation for the given sample data. How useful are the measures of variation for someone searching for a room? 242 197 115 118 245 145 268 110
-Range: $158 dollars -Standard Deviation: $65.8 dollars -Variance: $4328 dollars2 -The measures of variation are not very useful because when searching for a room, low prices, location, and good accommodations are not more important than the amount of variation in the area
Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation. Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general? 42 41 40 33 25 21 20 16 15.7 14.9
-Range: $27.1 million -Variance: $123.3 million -Standard Deviation: $11.1 million -The standard deviation is not a good estimate of variance because the sample is not representative of the whole population
Listed below are the measured radiation rates (in W\kg) corresponding to various cell phone models. If one of each model is measured for radiation and the results are used to find the measures of variation, are the results typical of the population of cell phones that are in use? Find the range, variance, and standard deviation of the given sample 1.43 0.73 1.45 0.82 0.99 1.13 0.72 1.33 0.56 1.33 1.45
-Range: 0.83 W/kg -Standard Deviation: 0.33 W/kg -Variance: 0.11 W/kg2 -The results for the measures of variation is not typical of the population of cell phones that are in use because some models of cell phones will have a longer market share than others. Measures from different models should be weighted according to their size in population
Listed below are foot lengths in inches for 11 randomly selected people taken in 1988. Are the statistics representative of the current population of all people? Find the range, variance, and standard deviation for the given sample data. 8.6 9.5 9.6 9.2 10.1 10.1 8.9 8.7 9 8.6 10.2
-Range: 1.6 inches -Standard Deviation: 0.62 inches -Variance: 0.38 inches2 -Since the measurements were made in 1988, it is not necessarily representative of the population today
Listed below are the numbers of hurricanes that occurred in each year in a certain region. The data are listed in order by year. Find the range, variance, and standard deviation for the given sample. What important feature of the data is not revealed by any of the measures of variation? 2 20 13 4 18 10 19 7 12 12 8 16 8 17
-Range: 18 hurricanes -Standard Deviation: 5.7 hurricanes -Variance: 32 hurricanes2 -The measures of variation reveal nothing about the pattern over time
Below are the jerseys numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us? 76 37 61 88 16 21 35 42 83 6 70
-Range: 82 -Standard Deviation: 28.5 -Variance: 810.1 -Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless
The brain volumes (cm3) of 20 brains have a mean of 1189.3cm3 and a standard deviation of 125.5cm3. Use the range rule of thumb to identify the limits seperating values that are significantly high or significantly low. For such data, would a brain volume of 1409.7cm3 be significantly high?
-Significantly low values are 938.9cm3 or lower -Significantly high values are 1439.7cm3 or higher -1409.7cm3 is not significantly high because it is between the limits seperating values
