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Chapter 3: Problem 6

Is it possible for a (quantitative) data set to have no mean, no median, or no mode? Give an example of a data set for which this summary measure does not exist.

Short Answer

Expert verified
In most quantitative data sets, we can calculate the measures of mean, median and mode. An exception to this is a data set with all unique values, where we cannot determine a mode since no value repeats. Also, an empty data set doesn't have a mean, median, or mode.

Step by step solution

01

Understanding Mean, Median, Mode

In statistical language, the mean is the average, calculated by adding all numbers in a data set and dividing by the amount of numbers in the set. The median is the mid-point value in a data set when the values are arranged in order, while Mode is the number which occurs most frequently in a data set.
02

Example for No Mode

Consider the data set: \[ \] {1, 2, 3, 4, 5}. Every number in this set appears once, so there isn't a mode here since no number appears more than once. This set, however, clearly has a mean (3) and median (3).
03

Example for No Mean and No Median

If you have an empty set, there will be no mean or median, as there are no values to calculate these summary measures. Obviously, there will be no mode for an empty set as well.

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Most popular questions from this chapter

Melissa's grade in her math class is determined by three 100 -point tests and a 200-point final exam. To determine the grade for a student in this class, the instructor will add the four scores together and divide this sum by 5 to obtain a percentage. This percentage must be at least 80 for a grade of \(\mathrm{B}\). If Melissa's three test scores are 75,69 , and 87 , what is the minimum score she needs on the final exam to obtain a B grade?

The following data represent the systolic blood pressure reading (that is, the top number in the standard blood pressure reading) in \(\mathrm{mmHg}\) for each of 20 randomly selected middle-aged males who were taking blood pressure medication. \(\begin{array}{llllllllll}139 & 151 & 138 & 153 & 134 & 136 & 141 & 126 & 109 & 144 \\ 111 & 150 & 107 & 132 & 144 & 116 & 159 & 121 & 127 & 113\end{array}\) a. Calculate the range, variance, and standard deviation for these data. b. Calculate the coefficient of variation.

For any data, the sum of all values is equal to the product of the sample size and mean; that is, \(\Sigma x=n \bar{x}\). Suppose the average amount of money spent on shopping by 10 persons during a given week is \(\$ 105.50 .\) Find the total amount of money spent on shopping by these 10 persons.

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The mean 2015 income for five families was \(\$ 99,520\). What was the total 2015 income of these five families?
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