Exam 2: Describing Data With Numerical Measures

When all the numbers in the data set are the same, the standard deviation, s, must be zero.

Which of the following best describes the relationship between the population mean and the sample mean?

Number of 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 Number of Calories in Soft Drinks statement. Find the outer fences.

Scores on a chemistry exam were mound-shaped with a mean score of 90 and a standard deviation of 64. Scores on a statistics exam were also mound-shaped, with a mean score of 70 and a standard deviation of 16. A student who took both exams achieved a grade of 102 on the chemistry exam and a grade of 77 on the statistics exam. Which of these may be inferred from the information given?

A data sample has a mean of 87 and a median of 117. The distribution of the data is positively skewed.

According to Tchebysheff's Theorem, which of the following bounds will delimit the fraction of observations falling within k (where ) standard deviations of the mean?

Expressed in percentiles, how is the interquartile range defined?

A parameter and a statistic can be used interchangeably.

Number of 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 Number of Calories in Soft Drinks statement. Find the inner fences.

The mode of a data set or a distribution of measurements, if it exists, is unique.

In all cases, the sum of the deviations of the measurements from their mean is 0.

The distribution of dollars paid for home insurance by home owners in Windsor is bell-shaped with a mean equal to $800 every six months, and a standard deviation equal to $120. Based on this information, we can use Tchebysheff's Theorem to determine the percentage of home owners who will pay between $560 and $1040 for home insurance.

Aptitude Tests Twenty-eight applicants interested in working in community services took an examination designed to measure their aptitude for social work. A stem-and-leaf plot of the 28 scores appears below, in which the first column is the count per "branch," the second column is the stem value, and the remaining digits are the leaves. Count Stems Leaves 1 4 6 1 5 9 4 6 3688 6 7 026799 9 8 145667788 7 9 1234788 -Refer to Aptitude Tests table. Construct a box plot for these data.

If, from a set of data, the sample mean was found to be 15 but the sample median was only 9, then the data set would be said to be skewed to the right.

Parasites in Foxes A random sample of 100 foxes was examined by a team of veterinarians to determine the prevalence of a particular type of parasite. Counting the number of parasites per fox, the veterinarians found that 65 foxes had no parasites, 20 had one parasite, and so on. A frequency tabulation of the data is given here: -Refer to the Parasites in Foxes statement and table. What fraction of the parasite counts fall within two standard deviations of the mean? Within three standard deviations? Do these results agree with Tchebysheff's Theorem? Do they agree with the Empirical Rule?

A distribution is said to be skewed to the right if the population mean is larger than the sample mean.

The Empirical Rule can be applied to any numerical data set.

Which of the following refers to numbers that indicate the spread or scatter of observations in a data set?

The interquartile range is the difference between the lower and upper quartiles.

Height of Basketball Players A sample of basketball players has a mean height of 190 cm, with a standard deviation of 12 cm. You know nothing else about the size of the data set or the shape of the data distribution. -Refer to the Height of Basketball Players statement. What can you say about the fraction of measurements that are less than 166?