Following are the speeds of 40 cars clocked by radar on a particular road in a
35-mph zone on a particular afternoon:
30, 36, 42, 36, 30, 52, 36, 34, 36, 33, 30, 32, 35, 32, 37, 34, 36, 31, 35, 20,
24, 46, 23, 31, 32, 45, 34, 37, 28, 40, 34, 38, 40, 52, 31, 33, 15, 27, 36, 40
Make (a) a frequency table and (b) a histogram. Then (c) describe the general
shape of the distribution.
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20 1
23 1
24 1
27 1
28 1
30 3
31 3
32 3
33 2
34 4
35 2
36 6
37 7
38 1
etc
normal around 36 mean
To create a frequency table and histogram for the given data, you need to follow these steps:
(a) Creating a Frequency Table:
1. Start by identifying the unique values in the data set.
In this case, the unique values are: 15, 20, 23, 24, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 42, 45, 46, 52.
2. Count the frequency of each unique value.
Go through the data set and count the number of occurrences for each unique value.
For example:
- The value 15 occurs once.
- The value 20 occurs once.
- The value 23 occurs once.
3. Create a table with two columns: one for the unique values and another for their corresponding frequencies.
Frequency Table:
| Speed | Frequency |
--------------------
| 15 | 1 |
| 20 | 1 |
| 23 | 1 |
| 24 | 1 |
| 27 | 1 |
| 28 | 1 |
| 30 | 3 |
| 31 | 4 |
| 32 | 3 |
| 33 | 3 |
| 34 | 5 |
| 35 | 2 |
| 36 | 6 |
| 37 | 2 |
| 38 | 2 |
| 40 | 4 |
| 42 | 1 |
| 45 | 1 |
| 46 | 1 |
| 52 | 2 |
(b) Creating a Histogram:
Now we will create a histogram using the frequency table.
1. On the x-axis, create bins (intervals) based on the unique values in the frequency table.
For example, you can use the unique values as bins: 15, 20, 23, 24, 27, 28, ..., 52.
2. On the y-axis, plot the frequency of each bin.
For instance, the frequency of the bin 15 would be 1, the frequency of the bin 20 would be 1, and so on.
3. Draw bars for each bin, where the height represents the frequency of that bin.
(c) Describing the General Shape of the Distribution:
To describe the general shape of the distribution, you need to visually analyze the histogram.
- Look for the center of the distribution: In this case, it seems to be around the value 34.
- Observe the spread or variability: The data ranges from 15 to 52, indicating a moderate spread.
- Examine the shape of the bars: The histogram appears to have a roughly symmetric shape, with a peak around the center and tails on both sides.
Overall, the distribution appears to be approximately symmetric and bell-shaped, resembling a normal distribution.