Question

1. the histogram you created has intervals of width 10 (like 40–50 and 50–60). use the set of axes and data to create another histogram with an interval of width 5. how does this histogram differ from the other one?

are you ready for more?
it often takes some playing around with the interval lengths to figure out which gives the best sense of the shape of the distribution.

1. what might be a problem with using interval lengths that are too large?
2. what might be a problem with using interval lengths that are too small?
3. what other considerations might go into choosing the length of an interval?

Explanation:

Question 1:

When interval lengths are too large in a histogram, they group too much data together. This causes the loss of detailed information about the data's distribution. For example, if intervals are very wide, differences in the frequency of data within smaller ranges are hidden, and the shape of the distribution (like peaks, valleys, or symmetry) becomes less clear or distorted. It becomes difficult to identify patterns such as where most data lies or if there are multiple clusters.

If interval lengths are too small, the histogram will have many narrow bars. This can make the distribution look very choppy and irregular, as random fluctuations in small subsets of data become more prominent. It becomes hard to see the overall pattern or trend in the data because the fine - grained intervals create a lot of noise. Also, it may be difficult to interpret, as the main features of the distribution (like the central tendency or spread) are obscured by the large number of bars, and the graph can look cluttered.

One consideration is the range of the data. If the data has a large range, larger intervals might be more manageable, but if the range is small, smaller intervals could be appropriate. The number of data points is also important; with a large number of data points, smaller intervals can be used to show more detail, while with a small number of data points, too - small intervals can be problematic (as in question 2). The purpose of the analysis matters too: if we want a broad overview, larger intervals are better, but if we need detailed insights, smaller intervals may be preferred. Also, the nature of the data (e.g., if it's continuous or discrete, and the precision of the data) can influence interval length choice. For example, if data is measured in whole numbers and is discrete, intervals should align with the possible values to some extent.

Answer:

Using interval lengths that are too large can hide detailed information about the data distribution, distort the true shape of the distribution (e.g., hide peaks or clusters), and make it difficult to identify patterns or differences in the frequency of data within smaller ranges.

Question 2: