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Chapter 3: Problem 39

Name two measures of the center of a distribution, and state the conditions under which each is preferred for describing the typical value of a single data set.

Short Answer

Expert verified
The two common measures of the center of a distribution are the mean and median. The mean, calculated as the sum of the data points divided by the total number of data points, is preferred for symmetric or 'normal' datasets without extreme values. The median is the middle value in an ordered data set and is preferred for skewed datasets or those with extreme values as it's less influenced by these values.

Step by step solution

01

Understand the concept of Mean as a measure of center

The mean, often referred to as the average, is calculated by adding all the data points in a dataset and dividing by the total number of data points. This measure is preferred when the dataset is 'normal' or symmetrical with no outliers, since the mean is sensitive to extreme values.
02

Understand the concept of Median as a measure of center

The median is the middle value in a data set when it's ordered in an ascending or descending manner. If there's an even number of observations, the median will be the average of two middle numbers. The median is preferred when we have an 'abnormal' dataset, especially with skewed data or when there are outliers, because it is not affected by extreme values.
03

State which measure is preferred under what condition

The mean is usually the preferred measure of center for symmetrically distributed data or data without outliers, as it takes into account all data points. On the other hand, the median is the preferred measure of center for skewed datasets or datasets with outliers, because it isn't influenced by extreme values to the same extent as the mean.

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Most popular questions from this chapter

Construct two sets of numbers with at least five numbers in each set (showing them as dotplots) with the following characteristics: The mean of set \(A\) is larger than that of set \(B\), but the median of set \(\mathrm{B}\) is larger than the median of set \(\mathrm{A}\). Label each dotplot with its mean and median in the correct place.

Distributions of delays in flight arrival of a particular airline are roughly bell-shaped. The mean delay in arrival time is 12 minutes, and the standard deviation is 4 minutes. Which is more usual, a flight arriving 4 minutes earlier than the mean delay time or a flight arriving 4 minutes after this time? Explain.

The number of leaves taken per year by employees of an office has a mean of 50 and a standard deviation of 5 . a. What number of leaves corresponds to a \(z\) -score of \(1.25\) ? b. What number of leaves corresponds to a \(z\) -score of \(-1.75\) ?

A teacher recorded the test score of a student in five different subjects. The maximum score for each subject is 50 . As you can see, a mistake was made in recording one entry. $$ 25,30,41,45,280 $$ When the mistake was corrected by removing the extra 0, will the median scores change? Will the mean change? Explain without doing any calculation.

The tenure of military coups in Argentina has been \(2,3,3,1,7\) and 7 years. (Source: Wikipedia) a. Find and interpret (report in context) the mean time of the coups, rounding to the nearest tenth. The mean time of the military coups in another South American country was \(1.3\) years. Did the military coups in Argentina tend to be longer than those in the other South American country? b. Find the standard deviation of the time, rounding to the nearest tenth. The standard deviation of the military coups in the other South American country was \(1.5\) years. Did the military rule in Argentina tend to have more or less variation than that in another country?
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