The bar graphs below show the percentage of students who received each score on their last English paper and Math test.  Determine whether each graph has a larger or smaller standard deviation.

10
20
30
40
50
English Score
60
70
80
90
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5
10
15
20
25
30
35
40
Math Score
60
70
80
90

To determine whether each graph (English Score and Math Score) has a larger or smaller standard deviation, we need to consider the spread of the scores. The standard deviation measures the dispersion of data points from the mean; a larger spread typically indicates a larger standard deviation.

**English Score:**
- Scores: 60, 70, 80, 90
- Frequencies (percentages): 8%, 56%, 30%, 6%

**Math Score:**
- Scores: 60, 70, 80, 90
- Frequencies: Not provided explicitly in your description, but they would need to be analyzed similarly.

**Analysis:**
1. **English Score:**
   - The English score distribution shows a moderate central concentration, with 56% of students scoring 70, but there's still a noticeable spread with students also scoring 60, 80, and 90.
   - The highest frequency (56%) is around the middle score, 70, but the other scores show significant dispersion, especially with the 6% at 90.

2. **Math Score:**
   - Since the exact percentages for Math Scores are not provided, let's assume that the Math graph follows a different distribution. If the Math scores are more tightly clustered around a single value, it would have a smaller standard deviation. If the scores are more spread out, it would have a larger standard deviation.

### Conclusion:
- **If the Math graph shows a tighter clustering around the mean (e.g., most students scored 70 with fewer scoring 60, 80, or 90),** the Math score would have a smaller standard deviation compared to the English score.
- **If the Math graph has scores spread out more evenly across 60, 70, 80, and 90,** it would have a larger standard deviation.

Since the English score distribution has a moderate spread with a high central concentration but some spread at the extremes, we might expect the standard deviation to be smaller if the Math graph is highly clustered. Otherwise, it could be larger or similar.

### Next Steps:
1. Do you have the exact frequency percentages for the Math scores?
2. Would you like a deeper explanation of standard deviation calculation?
3. Would you like a comparison of possible scenarios for the Math distribution?
4. Is there a specific part of the calculation you'd like to focus on?
5. Do you need help visualizing the standard deviation for different distributions?

**Tip:** The standard deviation is sensitive to outliers, so even small differences in extreme values can significantly affect it.

Explore the differences in standard deviation between English and Math scores. Understand how standard deviation measures the dispersion of data points from the mean. Analyze the distribution of scores and learn how to interpret their implications. Suitable for high school students studying statistics and data analysis.

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