Question

Use the data set $$ \\{2,11,8,10,6,11,7,14,20,9,1\\} . $$ What is the range? A. 3 B. 6 C. 15 D. 19

Short answer

D. 19

Step-by-step solution

Understand the Range

The range of a dataset is the difference between the maximum value and the minimum value in the dataset.

Identify the Maximum and Minimum Values

From the given dataset, identify the maximum and minimum values. The maximum value is 20 and the minimum value is 1.

Calculate the Range

Subtract the minimum value from the maximum value: \(Range = 20 - 1 = 19\)

Match with Given Options

Compare the calculated range to the given options. The correct answer is D. 19.

Key concepts

finding range

Understanding how to find the range in a data set is a fundamental concept in statistics.
The range helps us understand the spread or dispersion of the data points.
To find the range, follow these steps:

• Identify the maximum value in the data set.
• Identify the minimum value in the data set.
• Subtract the minimum value from the maximum value.

This gives the range, which represents the difference between the highest and lowest values.

maximum and minimum values

The maximum and minimum values in a data set are simply the largest and smallest numbers, respectively.
Identifying these values is critical because they are needed to calculate the range.
In the given exercise, the maximum value is 20 and the minimum value is 1.

To find these values, you can:

• Scan through the data set to spot the highest number (maximum value).
• Similarly, scan to find the lowest number (minimum value).

Knowing these values helps us move to the next step, which is calculating the range.

data set analysis

Data set analysis involves examining the data to draw meaningful insights.
One basic form of analysis is calculating the range, which tells us about the spread of the data.
For example, in this exercise, by finding that the range is 19, we know that there is a wide spread of values from the smallest to the largest.

Some steps to improve data set analysis include:

• Organizing the data in ascending or descending order.
• Identifying outliers or anomalies.
• Comparing the range with other statistical measures like mean, median, and mode.

These steps help in understanding the overall distribution and variability within the data.