) Explain why the sample midrange might be preferred to the sample mean as an estimator of the population mean.

In this exercise we have to analyze the graph informing and calculate the midrange, that is, the average between the highest and lowest value, so:

It is a good Estimator of the Population Mean because the distribution of the sample midrange is just same as the distribution of the random variable. So we can say the midrange value is .  

In this exercise, we have to analyze the graph informed in the question and from it observe what is requested, then:

The sample midrange can be computed as:

The sample midrange uses only a small portion of the data, but can be heavily affected by outliers. It provides information about the skewness and heavy-tailedness of the distribution which is just same as the distribution of the random variable. The nature of this distribution is not intuitive but the Central Limit in which it will approach a normal distribution for large sample size.

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It is a good Estimator of the Population Mean because the distribution of the sample midrange is just same as the distribution of the random variable.

Step-by-step explanation: from the table,

Minimum value = 34

maximum values = 1084

The sample mid-range can be computed as:

(Min.value + max.value)/2

(34 + 1084)/2

Sample mid-range = 55

The sample midrange uses only a small portion of the data, but can be heavily affected by outliers.

It provides information about the skewness and heavy-tailedness of the distribution which is just same as the distribution of the random variable.

The nature of this distribution is not intuitive but the Central Limit in which it will approach a normal distribution for large sample size.

37

step-by-step explanation: