Math Problem Statement

Does the histogram provide convincing evidence that the surveyed ages come from a normal distribution? Explain your answer.

Solution

The image shows a histogram representing the distribution of ages, with frequency on the vertical axis and age ranges on the horizontal axis. Additionally, the question asks if the histogram provides evidence that the surveyed ages come from a normal distribution.

Key observations from the histogram:

  1. The bars of the histogram represent different age intervals (from 30 to 80 years). The frequencies of each age group are given as 160, 160, 130, 115, 125, and 157 respectively (from left to right).
  2. A normal distribution is symmetric and bell-shaped, with most of the data centered around the mean, tapering off towards both ends.

Does the histogram suggest a normal distribution?

From the histogram:

  • The frequencies start high, dip slightly in the middle age ranges (around 50-60), and then rise again slightly at the higher age ranges (70-80).
  • This pattern suggests that the distribution is not symmetric, as the histogram does not have a clear peak and tapering at both ends. Instead, it shows two peaks and a dip in between.

Thus, the histogram does not strongly suggest that the ages come from a normal distribution because it lacks the typical bell-shaped curve that characterizes normality.

Would you like to explore more on normal distributions or related topics?

Here are 5 related questions:

  1. What are the key characteristics of a normal distribution?
  2. How can skewness and kurtosis help assess the normality of a dataset?
  3. What statistical tests can be used to confirm if a distribution is normal?
  4. How do outliers affect the shape of a distribution in histograms?
  5. What are the consequences of assuming normality when the data isn’t normally distributed?

Tip: When analyzing distributions, always consider both the shape of the histogram and summary statistics (like mean, median, and standard deviation) to get a clearer picture of the data.

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Math Problem Analysis

Mathematical Concepts

Statistics
Data Distribution
Normal Distribution
Histograms

Formulas

None (Visual Analysis of Histogram)

Theorems

Characteristics of Normal Distribution

Suitable Grade Level

Grades 10-12