Give an example of a set of data for which a stem and leaf
plot would be more informative than a histogram.
To provide an example of a set of data where a stem and leaf plot would be more informative than a histogram, let's consider a dataset of students' ages in a class.
Suppose we have the following ages of students: 18, 19, 20, 21, 23, 23, 23, 24, 26, 27, 30, 32, 34, 37, 39, 40, 42, 45, 46, 50.
Now, let's compare how a stem and leaf plot and a histogram would represent this data:
Stem and Leaf Plot:
The stem and leaf plot displays data by splitting the digits into stems and leaves. The tens place is represented by the stem, and the ones place is represented by the leaf. Here's how the stem and leaf plot for the given data would look:
1 | 8 9
2 | 0 1 3 3 3 4 6 7
3 | 0 2 4 7 9
4 | 0 2 5 6
5 | 0
Histogram:
A histogram represents data by grouping it into intervals or bins and displaying the frequency or count of observations within each interval. Here's how a histogram for the given data could look:
Age Range | Frequency
---------------------
15-20 | 3
20-25 | 4
25-30 | 2
30-35 | 2
35-40 | 3
40-45 | 2
45-50 | 2
In this case, a stem and leaf plot would be more informative than a histogram because the data set is relatively small and has distinct values. The stem and leaf plot shows each individual value, providing a clear picture of the distribution, while the histogram might unintentionally obscure the fact that some values occur multiple times.
By visualizing the data using a stem and leaf plot, you can easily identify the distribution, gaps, and potential outliers, leading to a better understanding of the dataset without the need for grouping or interval calculations as required in a histogram.