Question

the data set {7, 20, 51, 6, 30, 72, 31, 84, 28, 77, 98} is to be represented by a histogram. which first interval would most clearly and simply show the distribution of this data?

a. 0–5

b. 0–10

c. 0–50

d. 0–100

Explanation:

Step1: Analyze data points

The data set is {7, 20, 51, 6, 30, 72, 31, 84, 28, 77, 98}. Check which interval includes the smallest values (6,7) and is simple.

Step2: Evaluate each option

• Option A (0 - 5): 6 and 7 are not in this interval, so it's invalid.
• Option B (0 - 10): 6 and 7 are in this interval, and it's a simple, narrow interval to start showing distribution.
• Option C (0 - 50): Too broad initially, would group many values together, not clear for first interval.
• Option D (0 - 100): Extremely broad, would not show distribution clearly as most data would be in one interval.

Answer:

B. 0 - 10