Question

explain how to find the range of a data set. what is an advantage of using the range as a measure of variation? what is a disadvantage?

explain how to find the range of a data set. choose the correct answer below.
a. the range is found by subtracting the first data entry from the last data entry.
b. the range is found by adding the first and last data entries.
c. the range is found by adding the minimum and maximum data entries.
d. the range is found by subtracting the minimum data entry from the maximum data entry.

what is an advantage of using the range as a measure of variation?
a. it uses only two entries from the data set.
b. it is easy to compute.
c. it uses all entries from the data set.

what is a disadvantage of using the range as a measure of variation?
a. it is hard to compute.
b. it uses all entries from the data set.
c. it uses only two entries from the data set.

Explanation:

Part 1: How to find the range of a data set

To find the range, we identify the maximum (largest) and minimum (smallest) values in the data set. The range is calculated by subtracting the minimum value from the maximum value. Among the options:

• Option A: Subtracting first from last is incorrect (order of data doesn’t determine min/max).
• Option B: Adding first and last is wrong (range is a difference, not sum).
• Option C: Adding min and max is wrong (range is max - min).
• Option D: Subtracting minimum from maximum matches the formula \( \text{Range} = \text{Maximum} - \text{Minimum} \).

The range’s advantage is its simplicity. Calculating it only requires finding the max and min, then subtracting—this is quick and easy.

• Option A: “Only two entries” describes its calculation (max and min), but the advantage is ease, not just using two entries.
• Option B: “It is easy to compute” correctly identifies the main advantage (simple subtraction of max - min).
• Option C: “Uses all entries” is false (range only uses max and min).

The range’s main disadvantage is that it only depends on the maximum and minimum values (two entries), ignoring all other data points. This makes it sensitive to outliers and unrepresentative of overall data spread.

• Option A: “Hard to compute” is false (range is easy to compute).
• Option B: “Uses all entries” is false (range uses only two entries).
• Option C: “It uses only two entries from the data set” correctly identifies the disadvantage (ignores most data, so it may not reflect true variation).

Answer:

D. The range is found by subtracting the minimum data entry from the maximum data entry.

Part 2: Advantage of using range as a measure of variation