Cartoon Guide to Statistics and Chapter 3

¶ … Cartoon Guide to Statistics and Chapter 3 from Statistics in Plain English. You can assume your friend has read this material.

The concept "standard deviation" refers to how close or how far from the mean (i.e. The average person or thing) certain things or people that are studied are. To give an example: let's say you're studying people's pattern of diet and their calorie consumption per day. The mean stands for the average calorie consumption of the average amount of people studied. Study of the typical consumption will probably turn out to be normally distributed with most results clustered around the mean. Some people, however, may eat a lot less or a lot more and their distribution will be further away from the mean than that of others.

In the above shape (the normal bell structure), the standard deveiaiton (SD) is small because all clusters are obviously bunched together towards the middle (the mean). One skewed to the right or skewed to the left shows you where the tendency of the studied people leans to. If the curve were flatter and more dispersed, you will be able to see how spreads out the studied examples are from the average.

Part II: Show how to calculate the standard deviation from a small (15 -- 30 observations) set of data and interpret the value in the context of the problem. You should walk them through using the calculator and understanding the number which is produced rather than using the "by hand" formula.

Let's say we have 15 observations. (1) We total the sum of these 15 observations. (2) We total the mean of these 15 observations (by adding all of the numbers of the set and dividing the total by the number of items in your set). (3) We subtract the mean from each number and square result. Thusly: we subtract the mean from the first number in the data set, and square the differences, continuing with each number in the data set. (4) We find the mean of the differences. Add the squared differences and divide the total by the number of items (i.e. 15) in the set. (5) We take the square root of this mean of differences. The result is the standard deviation.

Part III: Discuss the part that standard deviation plays in using the Empirical Rule. Include a sample problem to illustrate the rule for your friend.

The 'Empirical rule' states that given a normal distribution (the normal bell-shaped pattern in the diagram above), almost all data will fall within 3 SD of the mean. In other words 68% of the sample studied will be one standard deviation removed from the mean, 95% of sample studied will be two standard deviations removed from the mean, and 99.7% will be three standard deviations removed from the mean.

Example for Empirical Rule

Find empirical rule for the values {12, 32,45,53,21,43}

Step 1: Calculate Mean

mean = (12+32+45+53+21+43)/6

mean = 206/6

mean = 34.33

Step 2: Find Standard Deviation

SD (?) =15.6162

Step 3: Apply Empirical Rule

68% of values are between 18.7171 to 49.9496

95% of Values are between 3.1009 to 65.5658