## Numerical Measures of Central Tendency and Variability

Read these sections and complete the questions at the end of each section. First, we will define central tendency and introduce mean, median, and mode. We will then elaborate on median and mean and discusses their strengths and weaknesses in measuring central tendency. Finally, we'll address variability, range, interquartile range, variance, and the standard deviation.

### Measures of Central Tendency

#### Mode

The mode is the most frequently occurring value. For the data in Table 1, the mode is 18 since more teams (4) had 18 touchdown passes than any other number of touchdown passes. With continuous data such as response time measured to many decimals, the frequency of each value is one since no two scores will be exactly the same (see discussion of continuous variables). Therefore the mode of continuous data is normally computed from a grouped frequency distribution. Table 2 shows a grouped frequency distribution for the target response time data. Since the interval with the highest frequency is 600-700, the mode is the middle of that interval (650).

Table 2. Grouped frequency distribution.

Range Frequency
500-600
600-700
700-800
800-900
900-1000
1000-1100
3
6
5
5
0
1

##### R code

td=c(37,33,33,32,29,28,28,23,22,22 ,22, 21,21,21, 20, 20, 19,19,18,18,18,18,16,15,14,14,14,12,12,9,6)

mean(td) [1] 20.45161

median(td)

[1] 20

quantile(td, probs = c(.5), type = 6)
50%
20

z=c(2, 4, 7, 12)

median(z)
[1] 5.5