Exam 2: Describing Data With Numerical Measures

A neighborhood 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 3 a. Find the average number of weekly sales of single scoop ice cream cones. ______________ b. Find the median number of weekly sales of single scoop ice cream cones. ______________ c. Find the variance for the weekly sales of single scoop ice cream cones. ______________

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.

A sample of 50 values produced the following summary statistics: Based on this information, the left and right ends of the box in a box and whisker plot are, respectively,

If a data set has 15 values that have been sorted in ascending order, which value in the data set will be the 25^th percentile?

Two students are enrolled in different sections of an introductory statistics class at a local university. The first student, enrolled in the morning section, earns a score of 76 on a midterm exam where the class mean was 64 with a standard deviation of 8. The second student, enrolled in the afternoon section, earns a score of 72 on a midterm exam where the class mean was 60 with a standard deviation of 7.5. If the scores on the midterm exams are normally distributed, which student scored better relative to his or her classmates? ____________________________ Explain. ________________________________________________________

The percentage of all observations in a data set that lies between the 30^th percentile and the third quartile:

In order to measure the variability in the same units as the original observations, we compute the sample variance.

The sample variance is approximately the average of the squared deviations of the measurements from their mean.

A sample of 600 values produced the following summary statistics: Based on this information, the lower fence on a box and whisker plot is:

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

Whenever a statistical population can be described, at least roughly, by the perfectly symmetrical, bell-shaped normal curve, we can estimate the percentages of all population values that lie within specified numbers of standard deviations from the mean with the help of:

The following ten scores were obtained on a 20-point quiz: 4, 5, 8, 9, 11, 13, 15, 18, 18, and 20. The teacher computed the usual descriptive measures of center (central tendency) and variability (dispersion) for these data, and then discovered an error was made. One of the 18's should have been a 16. Which one of the following measures, calculated on the corrected data, would change from the original computation?

The median equals the second quartile.

The following five-number summary for a sample of size 500 were obtained: Minimum = 250, and Maximum = 4,950. Based on this information, if you were to construct a box and whisker plot, the value corresponding to the upper fence is 10,200.

Since Tchebysheff's Theorem applies to any distribution, it is very conservative.

Which of the following statements is true?

The following data represent the number of small cracks per bar for a sample of eight steel bars: 4 6 10 1 3 1 25 8 Which, if any, of the observations appear to be outliers? Justify your answer. ____________________________

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

One advantage of using the median as a measure of center is that its value is not affected by extreme values.

Suppose that the distribution of actual weight of students in your university or college is thought to be symmetric. If the average weight is 168 pounds, what would the median weight be?