Exam 3: Descriptive Measures

Provide an appropriate response. -The amount of money, in dollars, that an employee of a bank spent on lunch on six randomly selected days yielded the following data set: $8,9,6,18,11,18$ Compute $\left( \sum x _ { i } \right) ^ { 2 }$ and $\sum x _ { i } ^ { 2 }$ . Explain the difference between the two quantities.

Which score has a higher relative position, a score of 299 on a test with a mean of 260 and a standard deviation of 26, or a score of 42 on a test with a mean of 40 and a a standard deviation of 4? (Assume that the distributions being compared have approximately the same shape.)

For a particular population, the _____________ mean is a constant and the ____________ mean is a variable.

Determine the quartile or interquartile range as specified. -The weights (in pounds)of 17 randomly selected adults are given below. Find the interquartile range. 144 165 187 143 119 132 127 156 179 159 180 202 114 146 151 168 173

The mean of a set of data is 126.02 and its standard deviation is 89.34. Find the z-score for a value of 386.67. Round your final answer to two decimal places.

Solve the problem. -A variable x has the possible observations shown below. Possible observations of xcolon -3 -1 0 1 1 2 4 4 5 Find the $z$ -score corresponding to an observed value of $x$ of 2 . Round the values of $\mu$ and $\sigma$ to one decimal place. Round your final answer to two decimal places.

Find the median for the given sample data. -The normal monthly precipitation (in inches)for August is listed for 20 different U.S. cities. 3.5 1.6 2.4 3.7 4.1 3.9 1.0 3.6 4.2 3.4 3.7 2.2 1.5 4.2 3.4 2.7 0.4 3.7 2.0 3.6 2.7 0.4 3.7 2.0 3.6

Find the mode(s)for the given sample data. -The table shows the country represented by the winner of the 10,000 meter run in the Summer Olympic Games in various years. Year Country 1912 Finland 1920 Finland 1924 Finland 1928 Finland 1932 Poland 1936 Finland 1948 Czechoslovakia 1952 Czechoslovakia 1956 USSR 1960 USSR 1964 United States 1968 Kenya 1972 Finland 1976 Finland 1980 Ethiopia 1984 Italy 1988 Morocco 1992 Morocco Find the mode of the country data.

Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place thanthat used for the observations. -18, 4, 22, 18

Use the empirical rule to solve the problem. -The weights, in kilograms, of 60 randomly selected female school children from Country A, ages 12-15 years old, are presented in increasing order in the following table: 35.3 37.6 38.1 38.8 38.9 39.0 39.1 40.2 41.2 41.2 41.3 41.7 42.1 42.1 42.1 42.3 42.6 42.7 42.8 43.2 43.3 43.3 44.1 44.3 44.5 44.8 45.1 45.1 45.2 45.4 45.4 45.6 45.8 45.8 46.0 46.2 46.3 46.6 46.6 47.1 47.3 47.5 47.6 47.7 48.1 48.1 48.3 48.3 48.4 48.6 48.6 48.8 49.0 49.6 50.3 51.0 51.9 52.9 52.9 57.4 Note: The sample mean and sample standard deviation of these weights are, respectively, 45.19 and 4.19.

Find the median for the given sample data. -2, 7, 15, 23, 35, 37, 48

Find the median for the given sample data. -In ten trips to Las Vegas, a person had the following net gains: \ 2630 \ 1235 \ 4893 \ 6071 \ 3446 \ 3714 \ 6676 \ 8031 \ 6934 \ 4569

Construct and interpret a boxplot or a modified boxplot as specified. -The weights (in pounds)of 30 newborn babies are listed below. Construct a boxplot for the data. 5.5 5.7 5.8 5.9 6.1 6.1 6.3 6.4 6.5 6.6 6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2 7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7

A teacher records the test scores for the 40 students in her class. Corresponding to each score, she calculates a z-score. Julia's z-score is -2.8. Should she be concerned? Explain your reasoning.

Find the mode(s)for the given sample data. -The weights (in ounces)of 14 different apples are shown below. 5.4 4.3 4.6 5.8 4.0 5.4 4.3 5.3 5.6 5.8 5.4 5.3 5.8 6.3

Identify potential outliers, if any, for the given data. -The normal monthly precipitation (in inches)for August is listed for 20 different U.S. cities. 0.4 1.0 1.5 1.6 2.0 2.2 2.4 2.7 3.4 3.4 3.5 3.6 3.6 3.7 3.7 3.9 4.1 4.2 4.2 7.0

Find the range for the given data set. -The owner of a small manufacturing plant employs six people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from Home to work. The six distances are listed below. 2.3 5.6 1.2 4.8 6.3 3.1

Determine the quartile or interquartile range as specified. -The weights (in pounds)of 18 randomly selected adults are given below. Find the third quartile, $\mathrm { Q } _ { 3 }$ 120 165 187 143 119 132 127 156 179 159 180 202 114 146 151 168 173 144

Construct and interpret a boxplot or a modified boxplot as specified. -The normal monthly precipitation (in inches)for August is listed for 20 different U.S. cities. Construct a boxplot for the data. 0.4 1.0 1.5 1.6 2.0 2.2 2.4 2.7 3.4 3.4 3.5 3.6 3.6 3.7 3.7 3.9 4.1 4.2 4.2 7.0

Explain in your own words the difference between a parameter and a statistic. Give examples of two statistics and two parameters.