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Without making any calculations, which distribution of data has the largest standard deviation?

A. [tex]\(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)[/tex]

B. [tex]\(1, 1, 1, 4, 4, 4, 4, 7, 7, 7\)[/tex]

C. [tex]\(1, 1, 4, 4, 4, 4, 4, 4, 7, 7\)[/tex]

D. [tex]\(1, 4, 4, 4, 4, 4, 4, 4, 4, 7\)[/tex]

Sagot :

GinnyAnsweridn
To determine which distribution of data has the largest standard deviation, we should compare the standard deviations of each distribution.

Here are the distributions and their respective standard deviations:

1. Distribution: [tex]\(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)[/tex]
- Standard Deviation: Approximately 2.683

2. Distribution: [tex]\(1, 1, 1, 4, 4, 4, 4, 7, 7, 7\)[/tex]
- Standard Deviation: Approximately 2.324

3. Distribution: [tex]\(1, 1, 4, 4, 4, 4, 4, 4, 7, 7\)[/tex]
- Standard Deviation: Approximately 1.897

4. Distribution: [tex]\(1, 4, 4, 4, 4, 4, 4, 4, 4, 7\)[/tex]
- Standard Deviation: Approximately 1.342

Comparing these standard deviations:
- The first distribution has a standard deviation of 2.683.
- The second distribution has a standard deviation of 2.324.
- The third distribution has a standard deviation of 1.897.
- The fourth distribution has a standard deviation of 1.342.

The largest standard deviation is 2.683, which corresponds to the first distribution: [tex]\(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)[/tex].

Thus, the distribution [tex]\(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)[/tex] has the largest standard deviation.
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