3. Describing Data Numerically
Mean
1:30 minutesProblem 2.3.39
Textbook Question
In Exercises 37– 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.
Verified step by step guidance1
Step 1: Observe the graph and note that the data is unimodal and symmetric, meaning it has one peak and the distribution is roughly balanced on both sides of the center.
Step 2: Recall the three measures of central tendency: mean, median, and mode. The mean is the average of all data points, the median is the middle value when data is ordered, and the mode is the most frequently occurring value.
Step 3: For symmetric distributions, the mean is typically the best measure of central tendency because it takes into account all data points and reflects the center of the distribution accurately.
Step 4: The mode, which represents the most frequent heart rate, could also be considered, but it may not fully represent the center of the data if the distribution is symmetric.
Step 5: Conclude that the mean is the best measure of central tendency for this data because the graph is symmetric and unimodal, ensuring the mean accurately represents the center of the distribution.
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