To determine whether it is reasonable to treat a histogram as a sample from an approximately normal population, you should consider several key characteristics of the histogram:
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Shape: The histogram should exhibit a bell-shaped curve that is symmetric about the mean. In an approximately normal distribution, most of the data points should cluster around the center, with fewer data points occurring as you move away from the center.
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Skewness: A normal distribution has no skewness. If the histogram shows significant skewness to the left or right, this suggests that the population may not be normal.
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Kurtosis: Normal distributions have a specific level of kurtosis (the "peakedness" of the distribution). If the histogram shows extremely high peaks or flat tails (either too sharp or too flat), it might indicate non-normality.
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Outliers: A presence of outliers in the histogram can affect the assessment of normality. A normal distribution should not have extreme outliers.
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Sample Size: A larger sample size can help in approximating normality due to the Central Limit Theorem, which states that the means of sufficiently large samples will be approximately normally distributed, regardless of the population's distribution.
If these characteristics align with what you observe in the histogram, it is reasonable to treat the data as coming from an approximately normal population. If you notice significant deviations from these characteristics, it might suggest that the population is not normal.
Without seeing the actual histogram, I can't provide a definitive answer, but following the steps above should help you make an informed assessment.