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Which data set has the greatest spread?

[tex]\[
\begin{array}{l}
\text{Set A: }\{84, 91, 87, 77, 94, 89, 74\} \\
\text{Set B: }\{89, 73, 84, 91, 87, 77, 94\} \\
\text{Set C: }\{73, 84, 89, 88, 77, 91, 87, 90\} \\
\text{Set D: }\{84, 89, 88, 82, 91, 87, 99\}
\end{array}
\][/tex]

A. Set A
B. Set B
C. Set C
D. Set D

Sagot :

GinnyAnswer
To determine which data set has the greatest spread, we need to calculate the range for each set. The range of a data set is the difference between the maximum and minimum values in the set. Here are the steps to find the range for each set and determine which set has the greatest spread:

1. Calculate the range for Set A:
- Maximum value in Set A: [tex]\( 94 \)[/tex]
- Minimum value in Set A: [tex]\( 74 \)[/tex]
- Range of Set A: [tex]\( 94 - 74 = 20 \)[/tex]

2. Calculate the range for Set B:
- Maximum value in Set B: [tex]\( 94 \)[/tex]
- Minimum value in Set B: [tex]\( 73 \)[/tex]
- Range of Set B: [tex]\( 94 - 73 = 21 \)[/tex]

3. Calculate the range for Set C:
- Maximum value in Set C: [tex]\( 91 \)[/tex]
- Minimum value in Set C: [tex]\( 73 \)[/tex]
- Range of Set C: [tex]\( 91 - 73 = 18 \)[/tex]

4. Calculate the range for Set D:
- Maximum value in Set D: [tex]\( 99 \)[/tex]
- Minimum value in Set D: [tex]\( 82 \)[/tex]
- Range of Set D: [tex]\( 99 - 82 = 17 \)[/tex]

Now that we have computed the ranges for each set:
- Range of Set A: [tex]\( 20 \)[/tex]
- Range of Set B: [tex]\( 21 \)[/tex]
- Range of Set C: [tex]\( 18 \)[/tex]
- Range of Set D: [tex]\( 17 \)[/tex]

Comparing these ranges, we see that the data set with the greatest spread is Set B, with a range of 21.

Thus, the answer is:

B. Set B
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