The problem shown in the image is about interpreting a histogram and selecting the correct statement that best describes the data.

Step-by-step analysis:

1. Histogram Overview: The histogram shows the frequency distribution of the number of hours spent standing up. On the x-axis, we have the number of hours (from 0 to 7), and on the y-axis, we have the frequency (ranging from 0 to 12).

2. Shape of the Distribution:

   • The bars decrease as we move from left (0 hours) to right (7 hours). The frequencies are higher on the left side of the graph and lower on the right, indicating a right-skewed distribution. In right-skewed distributions, most of the data is concentrated on the left side, with fewer larger values to the right.

3. Question Asked: The question asks which of the following statements best describes the distribution of the data. The answer choices deal with whether the data is symmetric or skewed (left or right) and what that implies about the mean and median.

4. Key Vocabulary:

   • Right-skewed distribution: The tail of the distribution extends more to the right (larger values), so the mean is typically greater than the median.
   • Left-skewed distribution: The tail extends more to the left (smaller values), so the mean is typically less than the median.
   • Symmetrical distribution: The data is evenly distributed, and the mean and median are roughly the same.

Evaluating the Answer Choices:

• Choice A: "The distribution of the data is symmetrical, so the mean and median are likely within 4-5 hours."

  • This is incorrect because the distribution is not symmetrical.

• Choice B: "The distribution of the data is skewed right, so the mean and median are likely within 5-6 hours."

  • This is incorrect because, while the data is right-skewed, the 5-6 hour range is too far right.

• Choice C: "The distribution of the data is skewed left, so the mean and median are likely within 5-6 hours."

  • Incorrect, because the data is not left-skewed; it's right-skewed.

• Choice D: "The distribution of the data is skewed right, so the mean and median are likely within 3-4 hours."

  • This is the correct answer. The data is right-skewed, and the mean and median should be on the lower side (around 3-4 hours), as most of the data is concentrated on the left side of the graph.

Final Answer:

Choice D is the correct answer: "The distribution of the data is skewed right, so the mean and median are likely within 3-4 hours."

Would you like more details or have any other questions?

Related Questions:

1. What is the difference between mean, median, and mode?
2. How does a right-skewed distribution affect the mean and median values?
3. Can a distribution be both skewed and symmetric? Why or why not?
4. What would a left-skewed histogram look like compared to this one?
5. How would you calculate the mean and median from a dataset like this?

Tip:

For a quick visual check of skewness, remember that right-skewed distributions have a longer tail to the right, while left-skewed distributions have a longer tail to the left.