The mode of a sample of numbers is the most frequently occurring value in the sample. One

way to remember this is to consider that mode means fashion in French, so the mode is the most

popular value in the data set. But the mode has several issues when it comes to summarizing the

centrality of observed values for continuous numerical variables. Often there are no exact

duplicates, so there is no mode. If there are any exact duplicates, they usually are not in the center

of the data. And if there is more than one value that is duplicated the same number of times, you

will have more than one mode.

So the mode is not a good summary statistic for sampled data. But it’s useful for characterizing a

population distribution, because it’s the value where the peak of the distribution function occurs. Some

distribution functions can have two peaks (a bimodal distribution), as shown earlier in Figure 9-2d,

indicating two distinct subpopulations, such as the distribution of age of death from influenza in many

populations, where we see a mode in young children, and another mode in older adults.

Considering some other “means” to measure central tendency

Several other kinds of means are useful measures of central tendency in certain circumstances. They’re

called means because they all calculated using the same approach. The difference is that each type of

mean adds a slightly different twist to the basic mathematical process.

INNER MEAN

The inner mean (also called the trimmed mean) of N numbers is calculated by removing the

lowest value (the minimum) and the highest value (the maximum), and calculating the arithmetic

mean of the remaining N – 2 inner values. For the sample of seven values of DBP from study

participants from the example used earlier in this chapter (which were 84, 84, 89, 91, 110, 114,

and 116 mmHg), you would drop the minimum and the maximum to compute the inner mean:

.

An inner mean that is even more inner can be calculated by making an even stricter rule. The rule

could be to drop the two (or more) of the highest and two (or more) of the lowest values from the data,

and then calculate the arithmetic mean of the remaining values. In the interest of fairness, you should

always chop the same number of values from the low end as from the high end. Like the median

(discussed earlier in this chapter), the inner mean is more resistant to extreme values called outliers

than the arithmetic mean.

GEOMETRIC MEAN

The geometric mean (often abbreviated GM) can be defined by two different-looking

formulas that produce exactly the same value. The basic definition has this formula:

We describe the product symbol Π (the Greek capital pi) in Chapter 2. This formula is telling you to

multiply the values of the N observations together, and then take the Nth root of the product. Using the