The following data set lists the number of letters in the
first 50 words in a newspaper article:
2, 5, 5, 9, 4, 4, 6, 7, 7, 6, 6, 6, 2, 5, 10, 7, 7, 6, 3, 5, 3, 2,
3, 3, 5, 4, 3, 4, 6, 5, 5, 6, 3, 2, 6, 4, 3, 5, 5, 7, 2, 3, 5, 5,
5, 7, 3, 2, 10, 3
a. Make a frequency table detailing the occurrence of
each word length.
b. Find the relative frequency of each word length
observed.
c. Make a dot plot of the data from this experiment.
d. Did you observe any clusters or outliers in the data?
Explain.
We do not do your work for you.
Count the number of words of each length to determine your frequency table. arrange in order of value, with smallest on left. The ordinate will indicate frequency. For example, 10 will have a frequency of 2. The relative frequency would be 10/total number of scores.
If you did not know this previously, it should give you a start.
To answer these questions, we need to analyze the given data set.
a. To make a frequency table, we need to count the occurrence of each word length in the data set. Here's how we can do it:
- First, sort the data set in ascending order:
2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 9, 10, 10
- Now, create a table with two columns: "Word Length" and "Frequency".
- Fill in the "Word Length" column with each unique word length from the sorted data set.
- Count the occurrence of each word length and fill in the "Frequency" column.
Here's the frequency table:
| Word Length | Frequency |
|-------------|-----------|
| 2 | 6 |
| 3 | 10 |
| 4 | 6 |
| 5 | 9 |
| 6 | 6 |
| 7 | 4 |
| 9 | 1 |
| 10 | 2 |
b. To find the relative frequency of each word length, we divide the frequency of each word length by the total number of words (50). Here's the relative frequency for each word length:
| Word Length | Frequency | Relative Frequency |
|-------------|-----------|--------------------|
| 2 | 6 | 0.12 |
| 3 | 10 | 0.20 |
| 4 | 6 | 0.12 |
| 5 | 9 | 0.18 |
| 6 | 6 | 0.12 |
| 7 | 4 | 0.08 |
| 9 | 1 | 0.02 |
| 10 | 2 | 0.04 |
c. To make a dot plot of the data, we can represent each data point with a dot along a number line. Here's how we can create a dot plot:
- Draw a number line using the minimum and maximum word lengths (2 and 10 in this case).
- Mark each word length on the number line.
- Place a dot above each mark to represent the occurrence of that word length.
The dot plot could look like this:
| 2 |
| 3 |
| 4 |
| 5 | • • • • •
| 6 | • • • • • •
| 7 | • • • •
| 8 |
| 9 | •
| 10 | • • |
d. To observe clusters or outliers in the data, analyze the dot plot. Clusters are when there is a group of data points close to each other, while outliers are extreme values that differ significantly from the other data points.
In this dot plot, we can observe a cluster around word lengths 3, 5, and 6 since there are more dots in those areas compared to others. However, there doesn't seem to be any outliers as no word length appears to be exceptionally distant from the rest.