Question

Standard Deviation

The standard deviation is a number that measures how far a typical observation is from the mean.

34.19 34.1% 0.1% 2,1% 2.1% 13.6% 13.6 0.1%

Run Applet

For this discussion activity, you will use an applet that deals with the standard deviation of a numerical data set.

Navigate to the Standard Deviation (Links to an external site.)Links to an external site. applet and follow these instructions:

1. Prepare the applet for use.
   • Select the “Add point” button and enter a value of 0 in the input box, then select “OK”.
   • Repeat the above step to enter the value 20.
   • Select the “Reset” button to remove the data points, but leave the axis between 0 and 20.
2. Create Set A.
   • Insert eight data points approximately evenly spaced between 0 and 20.
   • Record the standard deviation of Set A.
   • Select the “Reset” button to clear the data.
3. Create Set B.
   • Insert all eight data points very close to 10 on the number line.
   • Record the standard deviation of Set B.
   • Select the “Reset” button to clear the data.
4. Create Set C.
   • Insert four points close to 0 and four points close to 20.
   • Record the standard deviation of Set C.

Post

1. Which data set has the lowest standard deviation?
2. Which has the highest?
3. Is this what you expected? Why or why not?

Answer 1

• Set B has the lowest standard deviation.
• Set C has the highest standard deviation.
• Yes, this is expected. For all of the 3 dataset the mean will lie near to the value 10. We know that standard deviation is a measure indicating how scattered the observations are from their corresponding mean value for a certain dataset. Since the mean would be almost same in all the 3 cases (around 10) all we need to find the datasets with data-points being the most spread & least spread to find the dataset with highest & lowest standard deviation respectively. Clearly, for set B, the observations are clustered around 10 i.e. they are the closest to their mean as compared to the other sets. Hence set B has least standard deviation. In set A there are still some data points which are close to their mean (around 10) but for set C all the observations are either at the left end or the right end from the mean. Hence observations in set C are more spread out than that of set A. That is why set C has highest standard deviation.