1. Restaurateur measuring the volume of soup served: - Appropriate summary: Mean and standard deviation
2. Highway patrol officer recording the make of cars: - Appropriate summary: Mode
3. Researcher computing the yearly salary of all employees at a large company: - Appropriate summary: Median and quartiles
4. Actuary collecting data on reported age at death: - Appropriate summary: Median and quartiles
5. Researcher surveying the price of regular gas at all gas stations: - Appropriate summary: Mode
How did we arrive at these assertions?
Let's analyze each hypothetical study to determine the most appropriate summary statistic:
1. Restaurateur measuring the volume of soup served: - Appropriate summary: Mean and standard deviation
- Reasoning: The mean and standard deviation would be appropriate here as they provide information about the average volume of soup served and the variability in the serving sizes.
2. Highway patrol officer recording the make of cars: - Appropriate summary: Mode
- Reasoning: The mode is suitable in this case because it helps identify the most popular car type, which is the one that appears most frequently in the dataset.
3. Researcher computing the yearly salary of all employees at a large company: - Appropriate summary: Median and quartiles
- Reasoning: The median and quartiles are more appropriate in this scenario because the distribution of salaries may be skewed due to the chief officers' much higher salaries. The median provides a measure of central tendency that is less affected by extreme values.
4. Actuary collecting data on reported age at death: - Appropriate summary: Median and quartiles
- Reasoning: Similar to the salary example, the age at death may have a skewed distribution with outliers. The median and quartiles provide a robust summary that is less influenced by extreme values.
5. Researcher surveying the price of regular gas at all gas stations: - Appropriate summary: Mode
- Reasoning: The mode is suitable for identifying the most common price of regular gas, as it represents the value that occurs most frequently in the dataset.
Summarily, Mean and standard deviation are appropriate when the distribution is approximately normal and you want to capture information about the average and variability. Median and quartiles are suitable when dealing with skewed distributions or datasets with outliers, providing a robust summary of central tendency and spread. Mode is useful for identifying the most frequent value in a dataset, making it appropriate for categorical or nominal data.
Complete question:
For each of the hypothetical studies, determine if the data set would be better summarized by the mean and standard deviation, the median and quartiles, or the mode. At least one summary type will be used more than once. A restaurateur measures the volume of soup served in each cup of soup that is ordered on a specific day. A highway patrol officer records the make of a random subset of 200 cars traveling through a particular stretch of highway to determine the most popular car type A researcher computes the yearly salary of all employees at a large company. The chief officers have much higher salaries than the rest of the employees. An actuary collects data on the reported age at death for residents of her state. A researcher surveys the price of regular gas at all gas stations in his city to determine the most common price Answer Bank mean and standard deviation mode median and quartiles