Histogram and Box Plot Synthesis

00:00 7 marks

Consider the following two parts:

(a) A histogram is provided that summarizes a data set of test scores. Describe the overall shape of the distribution (e.g., symmetric, skewed), its central tendency, and variability. Provide clear reasoning based on the visual characteristics of the histogram.

(b) A box plot summarizing the same data set is presented. Compare the summary derived from the box plot with that from the histogram, noting any similarities and differences in the depiction of center, spread, and the presence of outliers.

Part a

4 minutes 3 marks

Question

The histogram provided summarizes the distribution of test scores. Describe the overall shape of the distribution (e.g., symmetric, skewed), identify the center (e.g., approximate median or mode), and comment on the spread (variability) of the data. Provide clear reasoning for your summary.

Hint Hint

Hint

Focus on the symmetry of the histogram and note any clusters or gaps that indicate the center and variability.

Answer Answer
Mark Scheme Mark Scheme
Explanation Explanation
Formula Booklet

Answer Answer

Complete Answer

Assuming the histogram shows a roughly symmetric distribution, the shape is approximately symmetric. The center is around the middle range of scores, and the spread is moderate, with balanced tails indicating similar variability on both sides of the center.

Mark Scheme Mark Scheme

Answer Explanation Answer Explanation

Formula Booklet

Part b

5 minutes 4 marks

Question

The box plot provides a summary of the same data through quartiles. Compare the information from the box plot with that from the histogram. In your answer, discuss similarities and differences in the depiction of the center, spread, and any potential outliers.

Hint Hint

Hint

Consider how the median, quartiles, and potential outliers in the box plot relate to the overall distribution shape and spread you observed in the histogram.

Answer Answer
Mark Scheme Mark Scheme
Explanation Explanation
Formula Booklet

Answer Answer

Complete Answer

Assuming both summaries are consistent, both the histogram and box plot suggest a similar central tendency and spread. However, the box plot explicitly shows the median and IQR, and clearly indicates any outliers, which are less obvious in the histogram.

Mark Scheme Mark Scheme

Answer Explanation Answer Explanation

Formula Booklet