Exam 3: Describing Data: Numerical Measures

i. An outlier is a data point that always occurs in the first quartile. ii. A student scored in the 85 percentile on a standardized test. This means that the student scored higher than 85% of the rest of the students taking the test. iii. The interquartile range is the difference between the values of the first and third quartile, indicating the range of the middle fifty percent of the observations.

A survey of passengers on domestic flights revealed these distances: What is the range (in kms)?

(i. The weekly sales from a sample of ten computer stores yielded a mean of $25,900; a median $25,000 and a mode of $24,500. The shape of the distribution is negatively skewed (ii) For the median (measure of central tendency), the data must be ranked before it is possible to determine it. (iii) If the sum of all the values of a distribution is divided by the number of values, the result is the arithmetic mean.

Measures of dispersion calculated from grouped data are

The mean, as a measure of central tendency, would be inappropriate for which one of the following?

i. In a negatively skewed distribution, the mean is always greater than the median. ii. In a negatively skewed distribution, the median occurs at the peak of the curve. iii. In a positively skewed distribution, the mode is greater than the median.

i. In a positively skewed distribution, the mean is always greater than the median. ii. In a negatively skewed distribution, the mode occurs at the peak of the curve. iii. In a negatively skewed distribution, the mode is greater than the median.

i. The interquartile range is the average of the values of the first and third quartile. ii. An outlier is a data point that always occurs in the first quartile. iii. A student scored in the 85 percentile on a standardized test. This means that the student scored lower than 85% of the rest of the students taking the test.

In the calculation of the arithmetic mean for grouped data, which value is used to represent all the values in a particular class?

Chebyshev's theorem states that: i. About 68% of the observation will lie within one standard deviation of the mean. ii. About 95% of the observations will lie within two standard deviations of the mean. iii. Virtually all (99.7%) will lie within three standard deviations of the mean.

(i. The median (measure of central tendency) cannot be determined if the distribution has an open-ended class. (ii) The measure of central tendency used to determine the average annual percent increase in sales from one time period to another is the geometric mean. (iii) The smallest measure of central tendency in a positively skewed distribution is the mode

The ages of a sample of telephones used in a small town hotel were organized into the following table: What is the sample variance?

Which one of the following is referred to as the population mean?

A telemarketing firm is monitoring the performance of its employees based on the number of sales per hour. One employee had the following sales for the last 20 hours (i) The median for the distribution of number of sales per hour is 5 sales per hour. (ii. The first quartile for the distribution of number of sales per hour is 4 sales per hour. (iii) For the distribution of number of sales per hour, 50% of the observations are between 3 and 7.5.

i. If a frequency distribution is open-ended, the variance cannot be determined. ii. The range cannot be computed for data grouped in a frequency distribution having an open end. iii. The standard deviation is the positive square root of the variance

The following are the weekly amounts of welfare payments made by the federal government to a sample of six families: $139, $136, $130, $136, $147 and $136. What is the range?

Which measures of central tendency are not affected by extremely low or extremely high values?

A large oil company is studying the number of gallons of gasoline purchased per customer at self-service pumps. The mean number of litres is 10.0 with a standard deviation of 3.0 litres. The median is 10.75 litres. What is the Pearson's coefficient of skewness?

i. A percentile divides a distribution into one hundred equal parts. ii. A student scored in the 85 percentile on a standardized test. This means that the student scored higher than 85% of the rest of the students taking the test. iii. The interquartile range is the difference between the values of the first and third quartile, indicating the range of the middle fifty percent of the observations.

i. A value that is typical or representative of the data is referred to as a measure of central tendency. ii. The arithmetic mean is the sum of the observations divided by the total number of observations iii. The value of the observation in the center after they have been arranged in numerical order is called the weighted mean