To select the most appropriate measures of center and spread for a histogram, you typically need to consider the shape of the distribution represented in the histogram:
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Mean and Standard Deviation are best used when the data is symmetrically distributed without outliers. They are sensitive to extreme values.
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Median and Interquartile Range (IQR) are more appropriate for skewed distributions or when outliers are present. The median is a measure of the center that indicates the middle value, and the IQR measures the spread of the middle 50% of the data, thus giving a better sense of dispersion without being affected by outliers.
Without seeing the actual histogram, if the distribution is skewed or has outliers, the recommended measures are:
- Median
- Interquartile Range (IQR)
If the distribution is symmetric and has no outliers, then:
- Mean
- Standard Deviation would be appropriate.
Based on common statistical practice without a specific histogram, the safest responses to choose would usually be:
- Median
- Interquartile Range
If you have more details about the histogram or the shape of the data distribution, you might consider different measures accordingly.