**Step 1 of 2 :**

The following histograms are for three different samples, each having the same sample size of at least 30. Select the correct statement concerning standard deviation.

123456789(a) 123456789(b)  123456789(c)

To compare the standard deviations of the three histograms, it's essential to consider the spread or variability of the data in each graph.

1. **Histogram (a)** appears to have a narrow concentration of values, meaning most of the data points are close to each other, implying **low variability**.
2. **Histogram (b)** likely has a moderate spread, with values spread out but not as extreme as the next histogram.
3. **Histogram (c)** shows the widest spread, indicating the data points are more spread out from the mean, which suggests **high variability**.

### Conclusion:
- The **standard deviation** measures how spread out the data is. A larger spread (more dispersion) corresponds to a higher standard deviation.
- Therefore, the standard deviations are likely in this order:
  - (c) has the **largest** standard deviation,
  - (b) has a **moderate** standard deviation,
  - (a) has the **smallest** standard deviation.

Would you like further details or have any questions?

### 5 Relative Questions:
1. How does the shape of a histogram affect the interpretation of standard deviation?
2. What is the relationship between the range of a dataset and its standard deviation?
3. Can two histograms with different shapes have the same standard deviation?
4. How does sample size impact the calculation of standard deviation?
5. What other measures of variability are commonly used in statistics?

### Tip:
Remember that standard deviation is sensitive to outliers, meaning extreme values can significantly increase it.

The following histograms are for three different samples, each having the same sample size of at least 30. Select the correct statement concerning standard deviation.

Analyze the standard deviation of three histograms with the same sample size of at least 30. Learn how the spread of data impacts the variability and standard deviation, with a focus on statistical concepts such as the empirical rule and data distribution patterns. Suitable for students in Grades 10-12.

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