Question

comparing ways to represent data
use the golf - tournament data below to complete parts (a) through (e).
ages of golfers participating in a golf tournament: 25, 28, 29, 30, 32, 33, 34, 34, 35, 35, 37, 38, 40, 42, 43, 43, 43, 44, 44, 45, 45, 46, 51, 57, 60, 63
a. use the data to create a dot plot.
b. create a stem - and - leaf plot for the data.
c. use the stem - and - leaf plot to create a histogram for the data.
d. what are the most effective ways to represent this data? why?
e. what range of ages do most golfers fall between? do you see any ages that are much larger or smaller than other ages?

Explanation:

Step1: Create dot - plot

1. Draw a number line that includes all the values in the data set (from 25 to 63).
2. For each age value in the data set, place a dot above the corresponding number on the number line. For repeated values, stack the dots.

Step2: Create stem - and - leaf plot

1. Determine the stems: The stems will be the tens digits of the age values. So, the stems will be 2, 3, 4, 5, 6.
2. For each stem, list the corresponding units digits (the leaves) in ascending order. For example, for the stem 2, the leaves are 5, 8, 9; for the stem 3, the leaves are 0, 2, 3, 4, 4, 5, 5, 7, 8; and so on.

Step3: Create histogram from stem - and - leaf plot

1. Group the data from the stem - and - leaf plot into intervals. For example, we can use intervals like 20 - 29, 30 - 39, 40 - 49, 50 - 59, 60 - 69.
2. Count the number of data points in each interval.
3. Draw a bar for each interval with the height of the bar equal to the frequency of data points in that interval.

Step4: Determine effective data representation

The dot - plot is effective for showing the exact number of occurrences of each value and for identifying outliers easily. The stem - and - leaf plot is good for showing the distribution of data and for quickly seeing the shape of the data (e.g., symmetric or skewed). The histogram is useful for visualizing the overall distribution of the data and comparing frequencies across intervals.

Step5: Analyze age range and outliers

1. By looking at the plots, we can see that most golfers fall between 30 and 49.
2. The ages 57, 60, 63 are relatively larger compared to most of the other ages, and there are no extremely small values compared to the rest of the data.

Answer:

a. Dot - plot is created as described in Step1.
b. Stem - and - leaf plot is created as described in Step2.
c. Histogram is created as described in Step3.
d. Dot - plot, stem - and - leaf plot, and histogram are all effective. Dot - plot for exact counts and outliers, stem - and - leaf plot for distribution shape, histogram for overall distribution and frequency comparison.
e. Most golfers are between 30 and 49. Larger values are 57, 60, 63.