Question

Answer the questions below.(a)The 10 members of the swim team completed the following numbers of laps at today's practice: 78,79,81,82,84,85,86,87,88,89.Which measure should be used to summarize the data?MeanMedianMode(b)A car dealer has used cars for sale for the following amounts: $3400,$3600,$3700,$3800,$3900,$4000,$4100,$4300,$7600.Which measure should be used to summarize the data?MeanMedianMode(c)A data set shows the age of each resident at Lakeview Retirement Home.Which measure gives the age shared by the most residents?MeanMedianMode

Answer 1

To summarize data accurately, one must choose between the mean, median, and mode based on the data's characteristics. Use mean for symmetric data without outliers, median for skewed data or when outliers are present, and mode to indicate the most frequently occurring value.

Step-by-step explanation:

When summarizing data, it's critical to select the measure that most accurately represents the characteristics of the data set.

Measures for Summarizing Data

1. For a data set with no extreme outliers and that is symmetrically distributed, the mean is typically the best measure of center.
2. If the data set is skewed or contains outliers, the median is often more representative of the central tendency.
3. The mode is most informative when the data has one or more values that repeat frequently and is especially useful in categorical data.

Applying these principles to the provided scenarios:

• Swim team laps: Given the data is closely grouped and without outliers, the mean would be most appropriate.
• Used car prices: The presence of the outlier ($7600) suggests the median would better summarize the central tendency.
• Age of residents: To find the most common age, the mode is the correct measure.

Answer 2

Explanation

(a) The first step is to arrange the numbers of laps in ascending order:

78, 79, 81, 82, 84, 85, 86, 87, 88, 89.