Exam 2: Describing Data With Numerical Measures

Which one of these values represents the upper quartile of the data set 10, 12, 16, 7, 9, 7, 41, and 14?

The mean of 40 sales receipts is $69.75 and the standard deviation is $10.25. Using Tchebysheff's Theorem, at least 75% of the sales receipts were between $49.25 and $90.25.

Cola Bottling When a machine dispensing cola at a bottling plant is working correctly, it dispenses a mean of 340 mL of cola per bottle, with a standard deviation of 6 mL. -Refer to the Cola Bottling statement. When the machine is working correctly, what percentage of the bottles will be filled with between 328 and 352 mL of cola?

If two data sets have the same range, the variances in both sets will be the same.

Assume that 75% of the households in Saskatchewan have incomes of $24,375 or below. Given this information, it is certain that the mean household income is less than $24,375.

You are given a sample of 8 measurements: 13, 11, 15, 16, 14, 14, 13, and 15. a. Calculate the range. b. Calculate the sample variance and standard deviation. c. Compare the range and the standard deviation. Approximately how many standard deviations equal the value of the range?

The average score for a class of 35 students was 70. The 20 male students in the class averaged 73. What was the average score for the 15 female students in the class?

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 variance for the weekly sales of single scoop ice cream cones.

The following five-number summary for a sample of size 500 was obtained: Minimum = 250, and Maximum = 4,950. Based on this information, the distribution of the data seems to be symmetric.

Two classes, one with 15 students and the other with 25 students, took the same test and averaged 85 points and 75 points, respectively. If the two classes were combined, the overall average score of the 40 students would be 80 points.

In a mound-shaped distribution, there is no difference in the values of the mean and the median.

The mode is generally used to describe large data sets.

z-scores exceeding 3 in absolute value are likely to occur.

The following data represent the scores for a sample of 10 students on a 20-point chemistry quiz: 16, 14, 2, 8, 12, 12, 9, 10, 15, and 13. Find the median and the sample mean.

The sample z-score is a measure of relative standing defined by . It measures the distance between an observation and the mean in units of the standard deviation.

The median is one of the most commonly used measures of variability.

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. Construct a relative frequency histogram for x, the number of parasites per fox.

The value (n + 1)/2 indicates the value of the median in an ordered data set, where n is the number of data values.

When data have been grouped (as in a frequency table, a relative frequency histogram, etc.), the class with the highest frequency is called the modal class, and the midpoint of that class is taken to be the mode.

The standard deviation is the positive square root of the variance.