Question

The U.S. Bureau of the Census reports on the number of households (in thousands) in each state. Some of the data are shown in the table. Is one measure of central tendency the most representative of the typical number of households in these states? Explain your reasoning. $$\begin{array}{|l|c|}\hline \text { State } & \text { Households } \\\\\hline \text { Arizona } & 1,687 \\\\\hline \text { Califomia } & 11,101 \\\\\hline \text { Colorado } & 1,502 \\\\\hline \text { Idaho } & 430 \\\\\hline \text { Montana } & 341 \\\\\hline \text { Nevada } & 619 \\\\\hline \text { New Mexico } & 619 \\\\\hline \text { Utah } & 639 \\\\\hline \text { Wyoming } & 184 \\\\\hline\end{array}$$

Short answer

To determine the most representative measure of central tendency (mean, median, or mode), each of these needs to be calculated and evaluated. Depending on the outliers and variations in the data, one of them may be more representative of the typical number of households in these states.

Step-by-step solution

Compute the Measures of Central Tendency

Calculate the mean, median, and mode from the given data. The mean is the sum of all values divided by the number of values. The median is the middle value when the data is arranged in increasing or decreasing order. The mode is the most frequently occurring value if there is one.

Evaluate Each Measure

Once computed, each measure of central tendency needs to be evaluated. If there are outliers in data, mean would drastically change but not median. Median gives the central point of data whereas mode gives the most common number.

Decide the Most Representative Measure

After evaluating each measure, the decision about which one is more representative can be made. Since the data has varying numbers, we can likely assume that one measure, possibly the mean or median, will be more representative of the typical number of households.