From the Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997

Measures of Spread Worksheet

Here are a few nice questions on standard deviation, based on a question Pat Ballew submitted to the ap-stat mailing list.

The original problem

A set of 11 data values has a mean of 8 and a standard deviation of 2. At least one of the data items is the value 8. If this single value is removed, without replacement from the data set, what will be the standard deviation of the remaining data? Either show all work or justify your answer.

Variations

Option 1:

Same question but offer multiple choice responses

The standard deviation:
a) increases; b) decreases, C) is unchanged D) Insufficient information is given

Option 2:

If a value of 12 is removed what is the impact (with same multiple choice answers)

Option 3:

Given numbers 8, 10, and 12, which could be removed and have the least impact on the standard deviation?