Exam 2: Describing Data With Numerical Measures

Motor Skills of Children The times required for 10 children to learn a particular motor skill were recorded as 9, 15, 23, 20, 16, 15, 24, 18, 10, and 20 minutes. -Suppose someone told you that each value of a data set of 5 measurements had been multiplied by 100 and the sample mean was calculated to be 17.20. What was the sample mean of the original data?

When the distribution is skewed to the left, then the mean > the median.

Which of the following is a property of a symmetric distribution?

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. What is the median score?

The mean and variance of a sample of n = 25 measurements are 80 and 100, respectively. Explain in detail how to use Tchebysheff's Theorem to describe the distribution of the measurements.

A sample of students who have taken a calculus test has a mean score of 78.2, a mode of 67, and a median score of 67. Based on this information, what may one deduce about the distribution of the test scores?

Solution Volumes An analytical chemist wanted to use electrolysis to determine the number of moles of cupric ions in a given volume of solution. The solution was partitioned into n = 30 portions of 0.2 mL each. Each of the n = 30 portions was tested. The average number of moles of cupric ions for the n = 30 portions was found to be 0.185 mole; the standard deviation was 0.015 mole. -Refer to the Solution Volumes statement. Suppose the chemist had used only n = 5 portions of the solution for the experiment and obtained the readings 0.18, 0.21, 0.20, 0.22, and 0.18. Would the Empirical Rule be suitable for describing the n = 5 measurements? Why?

Frequency Table Suppose you are given the following frequency table of ratings from 0 to 8: Assume that the sample mean and the sample standard deviation are 0.66 and 1.387, respectively. -Refer to the Frequency Table. Do the results of the previous question agree with Tchebysheff's Theorem?

You are given the data values 5, 10, 15, 20, and 25. If these data were considered to be a population, and you calculated its mean, you would get the same value as if these data were considered to be a sample from another larger population.

If a store manager selected a sample of customers and computed the mean income for this sample, what has he computed?

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

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

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. Should the Empirical Rule be applied to this data set?

Motor Skills of Children The times required for 10 children to learn a particular motor skill were recorded as 9, 15, 23, 20, 16, 15, 24, 18, 10, and 20 minutes. -Refer to Motor Skills of Children statement. Find the median time to learn this task.

While Tchebysheff's Theorem applies to any distribution, regardless of shape, the Empirical Rule applies only to distributions that are mound-shaped.

The range is considered the weakest measure of variability.

A sample of 20 observations has a standard deviation of 4. The sum of the squared deviations from the sample mean is 320.

The standard deviation is a measure of relative standing.

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. Calculate the sample variance, the lower and upper quartiles, and the IQR for these data.

Student Extroversion Thirty-three students were asked to rate themselves on whether they were outgoing or not using this five-point scale: 1 = extremely extroverted, 2 = extroverted, 3 = neither extroverted nor introverted, 4 = introverted, or 5 = extremely introverted. The results are shown in the table below: -Refer to the Student Extroversion statement and table. Find the percentage of measurements in the intervals and . Compare these results with the Empirical Rule percentages, and comment on the shape of the distribution.