Homework 3.2
Which measure of variation is most sensitive to extreme values?
Range
Below are the jersey 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? 23 31 30 79 85 68 42 38 82 9 8
Range=77 Sample standard deviation=28.8 Sample variance=829.4 What do the results tell us? Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
A group of adult males has foot lengths with a mean of 27.58 cm and a standard deviation of 1.45 cm. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 24.3 cm significantly low or significantly high? Explain.
Significantly low values are 24.68 cm or lower. Significantly high values are 30.48 cm or higher. The adult male foot length of 24.3 cm is significantly low because it is less than 24.68 cm.
For data sets having a distribution that is approximately bell-shaped, _______ states that about 68% of all data values fall within one standard deviation from the mean.
The Empirical Rule
Listed below are foot lengths in inches for 11 randomly selected people taken in 1988. Find the range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are the statistics representative of the current population of all people? 10.2 9 9.1 9.3 10.2 8.9 10.4 8.7 9.6 9.2 9.5
The range of the sample data is 1.7 inches. The standard deviation of the sample data is .58 inches. The variance of the sample data is . 32 inches squared . Are the statistics representative of the current population of all people? Since the measurements were made in 1988, it is not necessarily representative of the population today.
Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data. 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 32 21 20 17 13 12.7 11.5
The range of the sample data is $30.5 million. The variance of the sample data is 155.75 million The standard deviation of the sample data is $12.48 million Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in general? No, because the sample is not representative of the whole population.
A random sample of 10 subjects have weights with a standard deviation of 11.4733 kg. What is the variance of their weights? Be sure to include the appropriate units with the result.
The variance of the sample data is 131.6366 kg squared .
The square of the standard deviation is called the _______.
Variance
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 261.9 and a standard deviation of 65.2. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 196.7 and 327.1? b. What is the approximate percentage of women with platelet counts between 66.3 and 457.5?
a. Approximately 68% of women in this group have platelet counts within 1 standard deviation of the mean, or between 196.7 and 327.1. b. Approximately 99.7% of women in this group have platelet counts between 66.3 and 457.5.
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.24°F and a standard deviation of 0.43°F. Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.95°F and 99.53°F? b. What is the approximate percentage of healthy adults with body temperatures between 97.81°F and 98.67°F?
a. Approximately 99.7% of healthy adults in this group have body temperatures within 3 standard deviations of the mean, or between 96.95°F and 99.53°F. b. Approximately 68% of healthy adults in this group have body temperatures between 97.81°F and 98.67°F.
Identify the symbols used for each of the following: (a) sample standard deviation; (b) population standard deviation; (c) sample variance; (d) population variance.
a. The symbol for sample standard deviation is s. b. The symbol for population standard deviation is σ. c. The symbol for sample variance is s squared. d. The symbol for population variance is σ squared.
