Questions: Answer the questions below. (a) The 9 members of the swim team completed the following numbers of laps at today's practice: 26,78,80,83,84,85,86,89,91 Which measure should be used to summarize the data? Mean Median Mode (b) As part of the U.S. Census, the number of children is reported for each family in the U.S. Which measure gives the most common number of children for a U.S. family?

Solution Steps

(a) To determine which measure to use to summarize the data, we need to consider the distribution of the data. The mean is useful for normally distributed data, the median is useful for skewed data, and the mode is useful for categorical data or to find the most frequent value.

(b) To find the most common number of children for a U.S. family, we should use the mode, as it represents the most frequently occurring value in a dataset.

The mean is calculated by summing all the values and dividing by the number of values: \[ \text{Mean} = \frac{26 + 78 + 80 + 83 + 84 + 85 + 86 + 89 + 91}{9} = 78.00 \]

The median is the middle value when the data is ordered. For the given data: \[ 26, 78, 80, 83, 84, 85, 86, 89, 91 \] The median value is \(84.00\).

The mode is the value that appears most frequently. For the given data: \[ 26, 78, 80, 83, 84, 85, 86, 89, 91 \] The mode is \(26\), as it appears only once, but it is the smallest value in the dataset.

Given the data distribution, the median is the most appropriate measure to summarize the data because it is less affected by outliers and skewed data.

Final Answer