Exam 5: Numerical Descriptive Measures

The following data provide the hours of television viewing per week for a sample of 15 high school students in Darwin: 5 11 25 19 18 20 27 13 8 10 15 19 8 9 12 a. Determine the locations and values of the first, second and third quartiles. b. Calculate the interquartile range. c. Interpret the value of the interquartile range.

A sample of eight observations of variables x and y is shown below: x 5 3 7 9 2 4 6 8 y 20 23 15 11 27 21 17 14 Calculate the covariance and the coefficient of correlation, and comment on the relationship between X and Y.

A courier company is reviewing their delivery times. The following descriptive statistics relates to this courier company. The mean time for package delivery is 5 hours, the first quartile is 4 hours, the third quartile is 17 hours. This means that the 25% of the deliveries take more than 17 hours.

Data were obtained for the weight in grams, of a sample of 10 packets of sweetener, as found in cafés. 4.5 5 5.9 5.4 5.5 4.7 4.9 4.7 4.7 4.6 Find the range

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Compute the 8th decile of the data.

The following data represent the weights (in kilograms) of a sample of 30 horses: Weight 165 175 150 155 173 149 145 153 153 153 152 145 164 143 170 175 148 174 171 156 166 168 152 150 173 168 146 155 172 159 Find the median weight.

Which of the following statements is true? A The population mean is al ways greater than the sample mean. B The population mean is always smaller than the sample mean. C The population mean must always equal the sample mean. D The population mean may equal, be less than or greater than the population mean.

Data were obtained for the weight in grams, of a sample of 10 packets of sweetener, as found in cafés. 4.5 5 5.9 5.4 5.5 4.7 4.9 4.7 4.7 4.6 Find the mean, median and mode weight packet of sweetener and explain which is best measure of central location.

Explain the best measure of central location, for each of the following: a. Method of travelling to work. b. Average income of university students. c. Average weight of a 1kg bag of flour.

Lily has been keeping track of what she spends on eating out. The last week's expenditures for meals eaten out were $5.69, $5.95, $6.19, $10.91, $7.49, $14.53 and $7.66. The mean amount Lily spends on meals is $8.35.

A courier company is reviewing their delivery times. The following descriptive statistics relates to this courier company. The mean time for package delivery is 5 hours, the first quartile is 4 hours, the third quartile is 17 hours. This means that 75% of deliveries take more than 4 hours?

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Calculate the 1st quintile. (Hint: 1^st quintile is L₂₀)

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Compute the interquartile range of the data.

The following data represent the weights (in kilograms) of a sample of 30 horses: Weight 165 175 150 155 173 149 145 153 153 153 152 145 164 143 170 175 148 174 171 156 166 168 152 150 173 168 146 155 172 159 Determine the location and value of the 65th percentile of the weights.

The number of hours a college student spent studying during the final exam week was recorded as follows: 7 6 4 9 8 5 10 Compute the range, x, s² and s for these data. Express each number in appropriate units.

A supermarket has determined that daily demand for egg cartons has an approximate mound-shaped distribution, with a mean of 55 cartons and a standard deviation of 6 cartons. a. For what percentage of days can we expect the number of cartons of eggs sold to be between 49 and 61? b. For what percentage of days can we expect the number of cartons of eggs sold to be more than 2 standard deviations from the mean? c. If the supermarket begins each morning with a stock of 77 cartons of eggs, for what percentage of days will there be an insufficient number of cartons to meet the demand?

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Calculate the 4th decile of the data.

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Find the 60th percentile of the ages.

A sample of 16 observations has a standard deviation of 2. Which of the following is the sum of the squared deviations from the sample mean? A 60 B 64 C 30 D 16

What are the relative magnitudes of the mean, median and mode for a unimodal distribution that is: a. symmetrical? b. skewed to the left? c. skewed to the right?