What measures of center and spread are best used if the data is symmetrical and asymmetrical? Explain your reasoning.

If the data is symmetrical, then the mean is the best measure of central tendency to use, and the standard deviation is the best spread to use.

If the data is unsymmetrical, the median is the best measure of central tendency to use, and the inter-quarterly range is the best spread to use.

Step-by-step explanation:

An histogram for a symmetrical data will give a symmetrical shape, and the mean, median and mode will all be the same value. Therefore, the best measure of central tendency to use is the mean. The standard deviation shows how far away the values in a given data set are from the mean, and since the mean is used as the measure of central tendency in this case, the standard deviation should be used as the spread.

An histogram for a an asymmetric data set will give an asymmetric shape, and the mean is not always equal to the median. Therefore, the best measure of central tendency to use is the median. The inter-quarterly range shows the range of the middle 50% of a certain data, which is considered from the median value. Since the median is used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.

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