Archaeology The depths (in inches) at which 10 artifacts are foun...

3. Describing Data Numerically

Standard Deviation

Statistics

3. Describing Data Numerically

Standard Deviation

1:09 minutes

Problem 2.4.11a

Textbook Question

Archaeology The depths (in inches) at which 10 artifacts are found are listed.
20.7 24.8 30.5 26.2 36.0 34.3 30.3 29.5 27.0 38.5

a. Find the range of the data set.

Verified step by step guidance

Step 1: Understand the concept of range. The range of a data set is the difference between the maximum value and the minimum value in the set. It provides a measure of the spread of the data.

Step 2: Identify the maximum value in the data set. Look at the given depths: 20.7, 24.8, 30.5, 26.2, 36.0, 34.3, 30.3, 29.5, 27.0, 38.5. The maximum value is the largest number in this list.

Step 3: Identify the minimum value in the data set. Similarly, find the smallest number in the list of depths provided.

Step 4: Subtract the minimum value from the maximum value. Use the formula:

Range = Maximum - Minimum

Step 5: The result of this subtraction will give you the range of the data set. Ensure the units (inches) are included in the final interpretation of the range.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Range

The range is a measure of dispersion that indicates the difference between the maximum and minimum values in a data set. It provides a simple way to understand the spread of the data. To calculate the range, subtract the smallest value from the largest value. In this case, it helps to summarize the variability in the depths at which the artifacts were found.

Data Set

A data set is a collection of related values or observations that can be analyzed statistically. In this context, the data set consists of the depths at which the 10 artifacts were discovered. Understanding the structure of the data set is crucial for performing calculations like the range and for interpreting the results meaningfully.

Descriptive Statistics

Descriptive statistics are statistical methods that summarize and describe the main features of a data set. This includes measures such as mean, median, mode, and range. These statistics provide insights into the central tendency and variability of the data, making it easier to understand the overall pattern and characteristics of the artifacts' depths.

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Archaeology The depths (in inches) at which 10 artifacts are found are listed. 20.7 24.8 30.5 26.2 36.0 34.3 30.3 29.5 27.0 38.5a. Find the range of the data set.