Exam 2: Describing Data With Numerical Measures

In a time study, conducted at a manufacturing plant, the length of time to complete a specified operation is measured for each on n = 40 workers. The mean and standard deviation are found to be 15.2 and 1.40, respectively. a. Describe the sample data using the Empirical Rule. ________________________________________________________ b. Describe the sample data using Tchebysheff's Theorem. ________________________________________________________

A parameter and statistic can be used interchangeably.

The following data represents the sales (measured in $10,000) of seven real estate salespersons employed by a local agency: 23 34 56 47 45 60 249 Which measure of center, the mean or the median, would provide a better measure of the average sales of the company? ______________ Explain. ________________________________________________________

If a set of data has 120 values, the value of the 30^th percentile will be calculated using the 36^th and 37^th values in the data, when the data values have been arranged in ascending order.

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

Which of the following statements is true for a symmetric distribution?

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. a. Find the standard deviation of these values. ______________ b. Find the range, R. ______________

A college placement office conducted a survey of 100 engineers who had graduated from Stanford University. For these engineers, the mean salary was computed to be $72,000 with a standard deviation of $8,000. The percentage of these engineers who earn more than $96,000 or less than $48,000 is:

The mode is generally used to describe large data sets.

The time required for ten children to learn a particular motor skill was recorded as 9, 15, 23, 20, 16, 15, 24, 18, 10, and 20 minutes. a. Find the mean time to learn this task. ______________ b. Find the median time to learn this task. ______________ c. Based on the values of the mean and median in parts (a) and (b) above, are the measurements symmetric or skewed? ______________ Explain. ________________________________________________________

Quartiles divide the values in a data set into four parts of equal size.

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

If two data sets have the same range:

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 a. Find the average number of small cracks per bar. ______________ b. Find the standard deviation for the number of small cracks per bar. ______________

The following data represent the number of calories in 12 ounce cans of eight popular soft drinks: 124 144 147 146 148 154 150 234 Find the inner fences. ______________ Find the outer fences. ______________ Construct a boxplot for this data. Does the boxplot indicate the presence of any outliers? ______________

The following summary statistics were computed from a sample of size 250: . Based on this information, which of the following statements is correct?

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.

In a histogram, the proportion of the total area which must be to the right of the mean is:

Tchebysheff's Theorem applies only to data sets that have a mound-shaped distribution.

A sample of basketball players has a mean height of 75 inches and a standard deviation of 5 inches. You know nothing else about the size of the data or the shape of the data distribution. Which rule(s) can you use to describe the data? ______________ Explain. ________________________________________________________ Approximately what proportion of measurements will fall between 60 and 90? ______________ Approximately what proportion of measurements will fall between 65 and 85? ______________ Approximately what proportion of measurements will fall below 65? ______________