Based on the frequency distribution given in the table, let's analyze the data to choose the correct histogram and determine if the distribution appears to be approximately normal.

Frequency Distribution:

• Class A (39–44): Frequency = 1
• Class B (45–50): Frequency = 3
• Class C (51–56): Frequency = 7
• Class D (57–62): Frequency = 10
• Class E (63–68): Frequency = 5
• Class F (69–74): Frequency = 3
• Class G (75–80): Frequency = 2

This distribution shows that the highest frequency is centered around class D (57–62) and the frequency gradually decreases as we move away from this center.

Analysis of the Histograms:

Comparing this data pattern with the histograms provided in the image:

• Histogram D most accurately represents this pattern. It shows a peak around the middle class (D), with frequencies decreasing as we move to either side of the peak, which matches the given data.

Determining Normality:

A normal distribution typically appears as a symmetric bell-shaped curve, where most of the values cluster around a central peak and taper off equally on both sides. While the data has a peak in the center (class D), the decrease in frequency is not perfectly symmetric. However, it still follows a somewhat bell-shaped curve.

Based on the options provided, the answer to whether the data is approximately normal would be:

• Option D: Yes, it is approximately normal.

Would you like more details or have any other questions?

Related Questions:

1. What is the definition of a normal distribution?
2. How do you interpret the symmetry of a histogram in statistics?
3. What are some common characteristics of data that is not normally distributed?
4. What is the role of the mean and standard deviation in a normal distribution?
5. How can you check if a distribution is normal using statistical tests?

Tip: When analyzing histograms, always look for the shape of the distribution and check if it resembles a bell curve for normality!