A Data set had a mean of 15 and the values are very spread out what can be inferred about the standard deviation?

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11-07-2024
Mathematics

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A Data set had a mean of 15 and the values are very spread out what can be inferred about the standard deviation?

Sagot :

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ishtiak17 ishtiak17 · Answer 1 · 2024-07-11T08:56:39-04:00

Answer:

Step-by-step explanation: It is likely large. If a dataset has a mean of 15 and the values are very spread out, this suggests that the standard deviation is relatively large.

Here’s why:

1. **Mean and Spread Relationship**: The mean (average) of a dataset represents its central tendency. When it's stated that the values are "very spread out," it implies that the data points are not clustered closely around the mean but are rather widely distributed.

2. **Standard Deviation Definition**: Standard deviation measures the dispersion or spread of data points around the mean. A larger standard deviation indicates that the data points are spread out over a wider range of values from the mean.

3. **Inference**: Given that the mean is 15 and the values are spread out, we can infer that the standard deviation is high. This means that the individual data points are far from the mean on average, indicating a greater variability or dispersion in the dataset.

Therefore, the inference about the standard deviation is that it is large, reflecting the fact that the data points deviate significantly from the mean of 15.

Sagot :

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