L2 Practice Part 1
Completion requirements
Unit E: Statistics and Probability
Chapter 1: Statistics
Practice
Instructions: Click the Download File button to download a printable PDF of the questions. Answer each of the following practice questions on a separate piece of paper. Step by step solutions are provided under the Solutions tab.
You will learn the material more thoroughly if you complete the questions before checking the answers.
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Kami and Justine complete an experiment in science class to determine the average reaction rate of a chemical reaction. The results are recorded in the table below.
Trial Reaction Time (s)
1 7.5 2 7.7 3 7.1 4 6.8 5 7.9 6 4.8 7 7.4 8 2.5 9 8.0 10 7.7 11 7.5
- Calculate the mean to the nearest tenth.
- Plot the data. Circle and state any outliers.
- Calculate the trimmed mean to the nearest tenth.
- Which best represents the average of the data: the mean or the trimmed mean?
- Use the scatterplot to answer the questions below.
- Circle and state any outliers in the data.
- Calculate the mean.
- Determine the median.
- A student calculated the trimmed mean to be 14°C. The calculation is shown below.
- Calculate the trimmed mean.
- Which is closer in value to the median: the mean or the trimmed mean?
Kami and Justine complete an experiment in science class to determine the average reaction rate of a chemical reaction. The results are recorded in the table below.
| Trial | Reaction Time (s)
|
|---|---|
| 1 | 7.5 |
| 2 | 7.7 |
| 3 | 7.1 |
| 4 | 6.8 |
| 5 | 7.9 |
| 6 | 4.8 |
| 7 | 7.4 |
| 8 | 2.5 |
| 9 | 8.0 |
| 10 | 7.7 |
| 11 | 7.5 |
- Calculate the mean to the nearest tenth.
- Plot the data. Circle and state any outliers.
- Calculate the trimmed mean to the nearest tenth.
- Which best represents the average of the data: the mean or the trimmed mean?
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The mean is 6.8 seconds.
- The two outliers on the graph are circled. The outliers are (6, 4.8) and (8, 2.5).
- The data listed in ascending order are
2.5, 4.8, 6.8, 7.1, 7.4, 7.5, 7.5, 7.7, 7.7, 7.9, 8.0.
The two lowest values, 2.5 and 4.8, and the two highest values, 7.9 and 8.0, are removed to eliminate the outliers before calculating the trimmed mean.
The trimmed mean is 7.4 seconds.
- The trimmed mean is more accurate since the values of 2.5 s and 4.8 s are much lower than the other data values.
Use the scatterplot to answer the questions below.
- Circle and state any outliers in the data.
- Calculate the mean.
- Determine the median.
- A student calculated the trimmed mean to be 14°C. The calculation is shown below.
- Calculate the trimmed mean.
- Which is closer in value to the median: the mean or the trimmed mean?
- The outlier is circled on the graph. The outlier is (4, 25).
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The mean is 15.1°C.
- Arrange the data in ascending order.
11, 12, 13, 13, 14, 15, 15, 16, 17, 25
There are 10 data values. As there is an even number of data values, the median is the average of the two middle values; i.e., the fifth and sixth data values.
The median is 14.5°C.
- The student omitted the value of 25°C in calculating the trimmed mean. When a trimmed mean is calculated, and equal number of values from the top and bottom of the set of data must be removed to eliminate the outliers. In addition
to 25°C, the value of 11°C must also be omitted.
- Arrange the data in ascending order.
11,12, 13, 13, 14, 15, 15, 16, 17, 25
The trimmed mean is 14.4°C.
- The trimmed mean of 14.4°C is closer to the median of 14.5°C. There is a larger difference between the mean of 15.1°C and median of 14.5°C.