Weekly salaries (in dollars) for a sample of construction workers are listed.
1100 720 1384 1124 1255 976 718 1316
749 1062 1248 891 969 790 860 1100


a. Find the mean, median, and mode of the salaries. Which best describes a typical salary?

Verified step by step guidance

1. Step 1: To find the mean, calculate the sum of all the salaries and divide by the total number of salaries. Use the formula: $\mathrm{Mean}=\frac{\sum x}{n}$, where $\sum x$ is the sum of all salaries and $n$ is the number of salaries.
2. Step 2: To find the median, first arrange the salaries in ascending order. If the number of salaries is odd, the median is the middle value. If the number of salaries is even, the median is the average of the two middle values. Use the formula: $\mathrm{Median}=\frac{x}{}$_n/2 + x_{n/2 + 1}2 (for even $n$).
3. Step 3: To find the mode, identify the salary value(s) that appear most frequently in the dataset. If no value repeats, there is no mode. If multiple values repeat with the same highest frequency, the dataset is multimodal.
4. Step 4: Compare the mean, median, and mode to determine which best describes a typical salary. Consider the distribution of the data: if the data is symmetric, the mean and median will be close. If the data is skewed, the median may better represent a typical salary.
5. Step 5: Analyze the dataset for outliers or extreme values that might affect the mean. If outliers are present, the median might be a more reliable measure of central tendency for describing a typical salary.

Key Concepts

Mean

The mean is the average of a set of numbers, calculated by summing all values and dividing by the count of values. It provides a central value that represents the overall dataset but can be influenced by extreme values (outliers). In the context of salaries, the mean gives a general idea of what a typical salary might be, but it may not always reflect the most common salary.

Median

The median is the middle value in a sorted list of numbers. If the dataset has an odd number of observations, the median is the middle number; if even, it is the average of the two middle numbers. The median is particularly useful in salary data as it is less affected by outliers and provides a better representation of a 'typical' salary when the data is skewed.

Mode

The mode is the value that appears most frequently in a dataset. In salary analysis, the mode can indicate the most common salary among workers, which may differ significantly from the mean and median. Understanding the mode helps identify salary trends and common earnings within the group, providing insight into the distribution of salaries.