Statistics: By theNumbers

Numbers Data thatare actually collected are sometimes called "raw data". These are thenumbers that have been measured and recorded. Suppose we wanted to findout if playing background music improves the running speed of rats in amaze. In the experiment, 11 rats (rat #1 - rat #11) would run whilelistening to music and 11 rats (rat #12 - rat #22) would run withoutlistening to music. We would measure the time it takes each rat to runthrough the maze. The time (in seconds) for each rat to complete the mazeis recorded. Here are the raw data:

Now let's crunch somenumbers! The Mean The "mean" is what we usually think of as an "average". The mean issimply the sum of all the scores in a group divided by the total numberof scores. So, in our maze example: The mean of the music group is 11.1 + 18.3 + 18.2 + 22.8 + 11.4 + 33.3 + 18.8 + 26.3 + 29.7 + 28.5 +30.9 =22.7 11 The mean of the "no music" group is 23.2 + 22.6 + 10.3 + 15.7 + 11.9 + 9.9 + 11.1 + 29.3 + 34.2 + 23.6 +11.0=18.4 11 (Note that I have rounded off these numbers.)

The Median The median is another way to describe a set of numbers. The median is thescore that is exactly midway in the set of numbers. The easiest way tofind the median is to rank the numbers in order. If we rank thescores from the music group in the rat maze data, it would look like: 11.1, 11.4, 18.2, 18.3, 18.8, 22.8, 26.3, 28.5, 29.7, 30.9, 33.3 Therefore, the median (the midway score) is 22.8 because thereare five scores higher than 22.8 (26.3, 28.5, 29.7, 30.9, 33.3) and five scores lower than 22.8 (11.4, 12.1, 18.2, 18.3, 18.8). Why don't you determine the median of the "no music" group. Check youranswer: The median of the "no music" group is: Answer15.7 If you had an even number of scores in your data set (for example, themaze running times of 10 rats rather than 11 rats), the median would bethe midway point between the two middle numbers. For example, in the setof numbers: 1, 2, 4, 6, 17, 20; the median is: 4 + 6=5 2 When you have an odd number of scores, you don't even have to know how toadd and divide to find the median. All you have to do is rank the numbersfrom low to high and find the middle number.

Mode The mode is a third way to describe a set of numbers. The mode is veryeasy to find; it is the number that occurs most often. For examplein the set of numbers: 1, 4, 4, 4, 4, 4, 6, 6, 10, 11, 13,15 the mode is4 since it occurs the most times. The mode does not provide very muchinformation about a whole set of numbers. It only tells what scoreoccurs most frequently.

It is important to know the average of agroup of numbers, but there is still more information to be squeezed outof the raw data. For example, it is important to know how similar aparticular number is to the other numbers in the group. In other words,the amount of variation in the data can be determined. The two most commonways to describe variation are the range and the standard deviation. The Range The range is the difference between the highest value and the lowestvalue in a sample. For example, in the set of numbers:2, 2, 2, 7, 8, 9, 10, 11, 11, 15, 20, the range is: 20 - 2 = 18 Sometimes statisticians include the highest and lowest scores inthe range. In this case, you must add "1" to the calculation. In otherwords: 20 - 2 + 1 = 19 The range is very easy to calculate, but it really does not give you verymuch information because it ignores most of the data. The range is onlyconcerned with the highest and the lowest values. The Standard Deviation The standard deviation is a very common method used in science to describethe variability in a set of numbers. It examines the spread (variability)of each data point around the mean. The standard deviation increases withan increase in the variability of the data. If every score in the dataset are the same, then the standard deviation will equal zero.

Continue tolearn about statistics: how to collect data, how to analyzedata, howto graph data and how to lie withstatistics.

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