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Chapter 3: Q3 (page 91)

Measures of Center In what sense are the mean, median, mode, and midrange measures of “center”?

Short Answer

Expert verified
  • Mean is the central measure based on all observations.
  • Median is the observation at the center as per the measurements.
  • Mode is the value with the most frequency.
  • Midrange is the central measure based on two extreme observations only.

Step by step solution

01

Mean

Mean is the measure for the central location of the data set. It is obtained using the measure of each observation along with the count of observations.

Thus, mean finds the center of all observations through the measures.

02

Median 

Median determines the observation that divides the entire data set into two halves. Thus, 50% of observations are, respectively, lesser or greater than the median value.

Thus, median finds the central observation of the data set by arranging the observations as per the measurement.

03

Mode

Mode forms the center of all observations as per the corresponding frequencies or number of repetitions in the entire dataset.

Thus, mode is/are the observation(s) with the highest frequency.

04

Midrange

Midrange is mathematically the average of two values; the highest and lowest measuring observations.

Thus, midrange provides a tentative measure of central observation based on two extreme values of the data.

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Most popular questions from this chapter

Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question

Listed below are the highest amounts of net worth (in millions of dollars) of celebrities. The celebrities are Tom Cruise, Will Smith, Robert De Niro, Drew Carey, George Clooney, John Travolta, Samuel L. Jackson, Larry King, Demi Moore, and Bruce Willis.

What do the results tell us about the population of all celebrities? Based on the nature of the amounts, what can be inferred about their precision?

250 200 185 165 160 160 150 150 150 150

In Exercises 21–24, find the coefficient of variation for each of the two samples; then compare the variation. (The same data were used in Section 3-1.) 21.

Pulse Rates Listed below are pulse rates (beats per minute) from samples of adult males and females (from Data Set 1 “Body Data” in Appendix B). Does there appear to be a difference?

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Female: 64 84 82 70 74 86 90 88 90 90 94 68 90 82 80

In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.

Celebrity Net Worth Listed below are the highest amounts of net worth (in millions of dollars) of celebrities. The celebrities are Tom Cruise, Will Smith, Robert De Niro, Drew Carey, George Clooney, John Travolta, Samuel L. Jackson, Larry King, Demi Moore, and Bruce Willis. Are the measures of variation typical for all celebrities?

250 200 185 165 160 160 150 150 150 150

The Empirical Rule Based on Data Set 1 “Body Data” in Appendix B, blood platelet counts of women have a bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.4. (All units are 1000 cells/L.) Using the empirical rule, what is the approximate percentage of women with platelet counts

a. within 2 standard deviations of the mean, or between 124.3 and 385.9?

b. between 189.7 and 320.5?

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