Exam 2: Describing Data With Numerical Measures

A sample of n = 10 measurements consists of the following values: 15, 12, 13, 16, 11, 12, 14, 15, 11, and 13. Calculate the value of the standard deviation (s) and the range (R), and use R to approximate s. Is this a good approximation?

For distributions of data that are skewed to the left or right, the median would likely be the best measure of centre.

For larger sample sizes, a rough approximation for the sample standard deviation s is that s R/4, where R is the range.

Optometrist Customers The following values denote the number of customers handled by an optometrist during a random sample of four periods of one hour each: 4, 6, 2, and 5. -The following data represent scores on a 15-point aptitude test: 8, 10, 15, 12, 14, and 13. Subtract 5 from every observation and compute the sample variance for the original data and the new data. What effect, if any, does subtracting 5 from every observation have on the sample variance?

The left and right ends of the box in a box plot represent the 25th and 75th percentiles, respectively.

Incomes of workers in an automobile company in Ontario are known to be right-skewed, with a mean equal to $36,200. Applying Tchebysheff's Theorem, at least 8/9 of all incomes are in the range of $29,600 to $42,800. What is the standard deviation of those incomes from that mean?

If the mean value of a distribution is 85 and the median is 67, the distribution must be skewed to the right.

Amount of Food Sold Suppose the hourly dollar amount of food sold by a local restaurant follows an approximately mound-shaped distribution, with a mean sales level of $400 per hour and a standard deviation of $60 per hour. -Refer to the Amount of Food Sold statement. During what percentage of working hours does this restaurant sell between $280 and $520 worth of food per hour?

A random sample from an unknown population had a sample standard deviation of zero. From this piece of information, which one of the following is a reasonable conclusion?

Ice Cream Cone Sales A neighbourhood ice cream vendor reports the following sales of single-scoop ice cream cones (measured in hundreds of cones) for five randomly selected weeks: 5, 4, 6, 5, and 3. -Refer to the Ice Cream Cone Sales statement. Find the median number of weekly sales of single-scoop ice cream cones.

Expressed in percentiles, the upper quartile is the 75th percentile.

Measures of relative standing indicate the position of one observation relative to other observations in a set of data.

In a histogram, if the distribution is skewed to the right, the proportion of the total area that must be to the left of the median is more than 0.50.

A data set in which the mean and median are equal is said to be bimodal data.

Calories in Soft Drinks The following data represent the number of calories in 340 mL cans of a sample of 8 popular soft drinks: 124, 144, 147, 146, 148, 154, 150, and 234. -Refer to the Calories in Soft Drinks statement. Are these measurements of numbers of calories symmetric or skewed? Justify your conclusion.

Lily's score on her biochemistry text placed her at the 97th percentile. What does this mean?

Any unusually large observation (as measured by a z-score greater than 3), or any unusually small observation (as measured by a z-score smaller than -3) is considered to be an outlier.

Which of the following is a meaningful measure of centre when the data are qualitative?

The median equals the second quartile.

Numerical descriptive measures computed from sample measurements are called statistics.