Math Problem Statement

Which measures of central tendency should be used for the data set in the above histogram?

Group of answer choices

Mode

Mean

Median

Which measures of central tendency should be used for the data set in the above histogram?

Solution

The histogram provided is relatively symmetric and bell-shaped, which suggests that the data follows a normal distribution. In such cases, mean and median are typically appropriate measures of central tendency because they tend to be close or equal when the data is normally distributed. However, mode might also be useful if you're interested in identifying the most frequent value, but for a normally distributed or symmetric dataset, mode might not add as much value as the mean or median.

Therefore, the mean and median are the most appropriate measures of central tendency for this dataset.

Would you like more details, or have any questions?

Here are some related questions:

  1. How do you calculate the mean from a histogram?
  2. What is the significance of symmetry in choosing central tendency measures?
  3. How can you estimate the median from a histogram?
  4. Why is the mode less useful for a symmetric distribution?
  5. What are the effects of skewness on the mean, median, and mode?

Tip: For symmetric distributions, the mean and median are almost the same, but if the distribution is skewed, the median is often a better measure of central tendency than the mean.

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Math Problem Analysis

Mathematical Concepts

Central Tendency
Symmetry
Normal Distribution

Formulas

-

Theorems

Properties of Normal Distribution

Suitable Grade Level

Grades 9-12