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Chapter 12: Problem 38

In Exercises 37-44, find the midrange for each group of data items. \(11,6,4,0,2,1,12,0,0\)

Short Answer

Expert verified
The midrange of the dataset (11,6,4,0,2,1,12,0,0) is 6.

Step by step solution

01

Identify the Maximum and Minimum Values

Scanning through the dataset, identify the largest and smallest numbers. In the dataset (11, 6, 4, 0, 2, 1, 12, 0, 0), the maximum value is 12 and the minimum value is 0.
02

Calculate the Average of Maximum and Minimum Values

The midrange is defined as the average of the maximum and minimum values in the data set. To find the midrange, simply add the maximum value to the minimum value and divide by 2. In this case, the calculation would be \((12 + 0)/2\).
03

Calculate the Midrange

Performing the calculation from Step 2 gives the midrange. For the given dataset, this would be \(12/2 = 6\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Data Set Analysis
Understanding a data set involves examining a collection of numbers or values that represent information. In the example provided, the data set consists of the numbers: 11, 6, 4, 0, 2, 1, 12, 0, 0. When analyzing a data set, you should:
  • Look for patterns or significant values, such as recurring numbers.
  • Identify unique features like the highest or lowest values.
  • Consider the spread or range of the data.
This process is essential in extracting meaningful information about the group of numbers and helps in making calculations like the midrange.
Maximum Value
The maximum value of a data set is the highest number within that collection. In our example of 11, 6, 4, 0, 2, 1, 12, 0, 0, the maximum value is 12. Finding this number is crucial, as it represents the upper boundary of your data. To accurately identify the maximum value, you should scan through each number in the list, ensuring no larger number goes unnoticed. This element plays a critical role in calculations like the midrange, as it provides one of the two central figures needed to perform the required computation.
Minimum Value
Conversely, the minimum value is the lowest number within the data set. In the given data (11, 6, 4, 0, 2, 1, 12, 0, 0), the smallest value is 0. Identifying the minimum is similarly important as it gives you the lower boundary of the data. When seeking the minimum value, ensure you account for every integer, so no smaller number sneaks by. As with the maximum, the minimum is essential for calculating the midrange, providing the other half of the average calculation needed.
Average Calculation
The average calculation in the context of midrange involves finding the midpoint between the maximum and minimum values. The formula for midrange is simple yet effective: \[\text{Midrange} = \frac{\text{Maximum Value} + \text{Minimum Value}}{2} \]In our example, the midrange is calculated by taking the maximum value of 12 and the minimum value of 0: \[\frac{12 + 0}{2} = 6 \]This calculation showcases the balancing point of the data's range, offering insight into where the center of the distribution lies. Understanding how to compute the midrange allows for a quick assessment of data spread and central tendency, augmenting deeper statistical analyses.

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Most popular questions from this chapter

A set of data items is normally distributed with a mean of 60 and a standard deviation of 8 . In Exercises 33-48, convert each data item to a z-score. 40

In Exercises 1-8, find the percentage of data items in a normal distribution that lie a. below and b. above the given z-score. \(z=-1.2\)

In Exercises 9-16, find the percentage of data items in a normal distribution that lie between \(z=-2.2\) and \(z=-0.3\).

What does a \(z\)-score measure?

Describe the 68-95-99.7 Rule.
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