What is an appropriate scale and interval for this histogram?
Answer (1)
The appropriate scale and interval for the histogram are determined by analyzing the range of frequencies in the data. The scale must cover the minimum and maximum frequencies, and the interval should provide a reasonable level of detail. Among the given options, a scale of 0-15 and an interval of 5 is the most suitable.
Analyze the frequencies: minimum is 0, maximum is 11.
Evaluate the scales: 0-10 (insufficient), 0-15 (sufficient), 1-10 (insufficient), 1-15 (less ideal).
Choose the scale that covers the range and starts at 0: 0-15.
Select the corresponding interval: 5.
The scale should be 0-15, and the interval should be 5.
Explanation
Analyze the problem and data We are given a frequency table for a histogram and asked to determine an appropriate scale and interval for the histogram's y-axis (frequency). The x-axis intervals are already defined in the table (1-10, 11-20, ..., 91-100).
Determine the range of frequencies The frequencies in the table are 1, 0, 1, 1, 2, 4, 6, 11, 5, 4. The minimum frequency is 0 and the maximum frequency is 11. The scale of the histogram must cover this range.
Evaluate the given options Let's evaluate each of the given options:
Scale: 0-10, Interval: 10. This scale does not cover the maximum frequency of 11. So, this option is not appropriate.
Scale: 0-15, Interval: 5. This scale covers the range of frequencies (0 to 11). The interval of 5 is reasonable.
Scale: 1-10, Interval: 5. This scale does not cover the minimum frequency of 0. So, this option is not appropriate.
Scale: 1-15, Interval: 10. This scale covers the range of frequencies, but it starts at 1 instead of 0, which is less ideal since we have a frequency of 0. Also, an interval of 10 might be too large, potentially hiding variations in the data.
Select the most appropriate option Based on the analysis, the most appropriate scale and interval for the histogram is a scale of 0-15 and an interval of 5. This covers the entire range of frequencies and provides a reasonable level of detail.
Examples
Histograms are commonly used to visualize the distribution of data, such as exam scores in a class. If you want to create a histogram of exam scores ranging from 0 to 100, and the highest number of students scoring in any 10-point range is 15, then a scale of 0-15 with intervals of 5 would be appropriate for the y-axis (number of students). This allows you to clearly see how many students scored in each range (e.g., 60-69, 70-79, etc.).
