3. Describing Data Numerically
Describing Data Numerically Using a Graphing Calculator
2:27 minutesProblem 4.CRE.1cd
Textbook Question
Cloud Seeding The “Florida Area Cumulus Experiment” was conducted by using silver iodide to seed clouds with the objective of increasing rainfall. For the purposes of this exercise, let the daily amounts of rainfall be represented by units of rnfl. (The actual rainfall amounts are in or )
Find the value of the following statistics and include appropriate units based on rnfl as the unit of measurement.
[Image]
c. midrange
d. range
Verified step by step guidance1
Step 1: Understand the problem. The midrange is the average of the smallest and largest values in a dataset, while the range is the difference between the largest and smallest values. Both are measures of data spread and central tendency.
Step 2: Identify the dataset. Locate the daily rainfall amounts (in units of rnfl) provided in the problem or accompanying image. If the dataset is not explicitly given, ensure you have access to it before proceeding.
Step 3: Calculate the midrange. Use the formula: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Midrange</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mi>Max</mi><mo>+</mo><mi>Min</mi><mo>)</mo></mrow><mn>2</mn></mfrac></math>. Here, 'Max' is the largest value in the dataset, and 'Min' is the smallest value. Add these two values and divide by 2. The result will be in units of rnfl.
Step 4: Calculate the range. Use the formula: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Range</mi><mo>=</mo><mi>Max</mi><mo>-</mo><mi>Min</mi></math>. Subtract the smallest value (Min) from the largest value (Max) in the dataset. The result will also be in units of rnfl.
Step 5: Interpret the results. The midrange provides a measure of central tendency, while the range indicates the spread of the data. Ensure that both results are reported with the appropriate units (rnfl) to maintain clarity and context.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Midrange
The midrange is a measure of central tendency that is calculated by taking the average of the maximum and minimum values in a data set. It provides a simple way to summarize the data by identifying a central point, but it can be sensitive to outliers, which may skew the result. In the context of rainfall data, the midrange would be expressed in the same units as the rainfall measurements.
Range
The range is a measure of dispersion that indicates the difference between the highest and lowest values in a data set. It provides insight into the variability of the data, showing how spread out the values are. For rainfall data, the range is calculated by subtracting the minimum rainfall amount from the maximum, and it is expressed in the same units as the rainfall measurements.
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Units of Measurement
Units of measurement are standard quantities used to express and compare physical quantities. In the context of rainfall, units such as millimeters or inches are commonly used to quantify the amount of precipitation. Understanding the appropriate units is crucial for accurately interpreting statistical results, such as midrange and range, ensuring that comparisons and calculations are meaningful.
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