Question

You work for a large farm with many fields of corn. You are investigating the mass of a sample of ears of corn. You gather the following data and enter it into your spreadsheet-Geogebra:

Mass(g) of ears of corn

15.0	13.3	20.4	26.1	28.7	19.6	18.6	15.7	18.6	14.7	16.9
16.7	20.2	17.3	21.1	23.1	19.6	16.1	25.6	22.2	16.7	15.4

Some of the masses in the sample seem much larger than the rest. You decide to make several calculations describing the "spread" of the data set. You hope to use them to help in the search for outliers.

Start with the IQR:

Apply the 1.5 IQR rule to search for outliers. Report the lower and upper cuttoffs.

Now find the mean and Standard deviation:

Apply the 2-standard deviation rule to search for outliers. Report the lower and upper cuttoffs.

1. IQR =
2. Lower:
3. Upper:
4. Are there any outliers by the 1.5 IQR rule? (Enter "yes" or "no")

Now find the mean and Standard deviation:

1. sample standard deviation

Apply the 2-standard deviation rule to search for outliers. Report the lower and upper cuttoffs.

1. Lower:
2. Upper:
3. Are there any outliers by the 2-standard deviation rule? (Enter "yes" or "no")

Answer 1

a) From the given data, we arrange the data in Ascending order as follows:

As per Above infromation

a) IQR = 5.675
b) Lower: 7.738
c) Upper: 30.438
d) Correct answer: No since all points are lies between Lower and Uppler limits

Now find the mean and Standard deviation:

Lower: Mean - 2 SD = 19.475 - 2 * 4.0931 = 11.2888
Upper: Mean + 2 SD = 19.475 + 2 * 4.0931 = 27.6612
Correct answer: Yes, since the number of observations greater than 27.6612 in the data is 1 i.e. 28.7

There is one outlier in the data