Exam 3: Describing Data: Numerical Measures

(i. The median (measure of central tendency) cannot be determined if the distribution has an open- Ended class. (ii. The measure of central tendency used to determine the average annual percent increase in Sales from one time period to another is the geometric mean. (iii) The smallest measure of central tendency in a positively skewed distribution is the mode

Sometimes, data has two values that have the highest and equal frequencies. In this case, the Distribution of the data can best be summarized as

(i. Correct to two decimal places, the sample standard deviation is approximately 25.99. (ii. Correct to two decimal places, the sample variance is approximately 675.25. (iii) The range is approximately 125.

The printout below is a summary of the average annual earnings of male full time workers in Canada from 1999-2008. Determine the coefficient of variation.

Using the information gathered for real estate prices in Regina and surrounding areas in the early 2000's, determine the standard deviation of the selling prices at that time.

Chebyshev's theorem states that: i. About 68% of the observation will lie within one standard deviation of the mean; ii. About 95% of the observations will lie within two standard deviations of the mean; iii. Virtually all (99.7%) will lie within three standard deviations of the mean.

A sample of the daily production of transceivers was organized into the following distribution. What is the mean daily production?

Which measures of central tendency always have but one value for a set of grouped or ungrouped Data?

The Investment Company Institute reported in its Mutual Fund Fact Book that the number of mutual Funds increased from 410 in 1990 to 857 in 2000. What is the geometric mean annual percent Increase in the number of funds?

A bottling company offers three kinds of delivery service - instant, same day and within five days. The profit per delivery varies according to the kind of delivery. The profit for an instant delivery is Less than the other kinds because the driver has to go directly to a grocery store with a small load And return to the bottling plant. To find out what effect each type of delivery has on the profit Picture, the company has made the following tabulation based on deliveries for the previous Quarter. What is the weighted mean profit per delivery?

(i. The research director of a large oil company conducted a study of the buying habits of Consumers with respect to the amount of gasoline purchased at full-service pumps. The arithmetic Mean amount is 11.5 gallons and the median amount is 11.95 litres. The standard deviation of the Sample is 4.5 litres. The Pearson's coefficient of skewness can be calculated to be -0.30. (ii. The Pearson's coefficient of skewness (Sk) measures the amount of skewness and may range From -3.0 to +3.0. It is computed by subtracting the median from the mean, multiplying the result by 3 and dividing by the variance. (iii) A study has been made of the number of hours a light bulb will operate before it burns out. If the Variance of this distribution were computed, it would be measured in hours squared

(i. Five students were given a page of problems with the instructions to solve as many as they could In one hour. Five students solved the following number of problems: 12, 10, 8, 6 and 4. The Arithmetic mean number of minutes required per problem is 7.5 minutes (average of 8 problems in An hour). (ii. David Electronics had a profit of $10 million in 1998. Profit doubled from 1998 to 1999 and profit Increased eight fold from 1999 to 2000. The annual geometric mean rate of growth from 1998 to 2000 was 200% (3 fold). (iii) The difference between the highest and the lowest value in a set of data is called the range.

(i. The range for laminate flooring is 0 or none. (ii. The standard deviation for nylon carpet is 4.64 cents (iii) The range for nylon carpet is $0.15 or 15 cents.

i. In a negatively skewed distribution, the mean is always greater than the median. ii. In a negatively skewed distribution, the median occurs at the peak of the curve. iii. In a positively skewed distribution, the mode is greater than the median.