calculating descriptive stats

Once you’ve been doing statistics for a while, you tend to take descriptive statistics for granted…mostly because we all use stats programs that just take our raw data and do it for us.

But for all of you who are just starting out, a thorough understanding of descriptive statistics is absolutely essential. So this is a quick post that will start from the ground up on descriptive stats.



measures of central tendency

Measures of Central Tendency

In statistics, we have this big collection of raw data from individuals, and we are always trying to describe the data set as a whole. Thus, we use “descriptive” statistics.

Measures of central tendency are commonly used method to describe data sets. Essentially, we are taking this collection of data and trying to explain where the “middle” of the data is. The three main measures of central tendency are the
mean, median, and mode.

Mean: Mean is just our fancy statistical way of saying average, and the calculation is quite simple: you add up all of the raw scores, and then divide by the number of scores that you added together.So let’s say that you bowl a lot, and you want to know your average score for the last five games you bowled. Your scores for each game were 150, 175, 250, 210, 195.

In order to calculate this, you would add the scores for each of those five games (150+175+250+210+195=980).

Now, you divide the sum of raw scores by the number of games (980/5 = 196). So your bowling average for the past 5 games was 196.

Median: The median is simply the “middle” number in the data set. If you rank your scores in order from high to low, the one that falls right in the middle represents the median. So if we refer back to our bowling example, the median is 195 because that is the “middle” score on the number line.

150     175     195     210     250

Mode: The mode is the most common score/value in the data set. In our bowling example, all of the scores have a frequency of 1 (i.e., the only occur one time), so there is no mode. But let’s say that we are talking about the age of high school seniors (see below). In this sample of ten students, the most common age is 17.5…So mode = 17.5.

17       17.25       17.5       17.5        17.5       18       18       18.5       18.5       19