The following data set has values: 100, 105, 110, 115, 120. What is the range?
Correct Answer
A) 20
Why this is correct: In statistics, the range is a measure of dispersion calculated as the difference between the maximum and minimum values in a data set. For the set [100, 105, 110, 115, 120], the highest value is 120 and the lowest is 100. Therefore, the range is 120 minus 100, which equals 20. Why the other choices are wrong: 550 is the sum of all values (100+105+110+115+120), not the range. 110 is the mean (sum 550 divided by 5) and the median (middle value), not the range. 10 is an incorrect calculation; it might result from misidentifying the highest and lowest values or from a simple subtraction error. Exam tip: For range questions, always first identify the largest and smallest numbers. The calculation is always: Range = Maximum Value - Minimum Value.
Why This Is the Correct Answer
Option B (20) is correct because range is calculated by subtracting the lowest value from the highest value in the data set. In this case, the highest value is 120 and the lowest value is 100. Therefore, the range equals 120 - 100 = 20. This simple calculation gives us the total spread of the data from minimum to maximum.
Why the Other Options Are Wrong
Option B: 550
Option B (550) appears to be the sum of all values in the data set (100+105+110+115+120=550), which is used to calculate the mean, not the range.
Option C: 110
Option C (110) represents the median or middle value of this data set, not the range. The median is a measure of central tendency, while range is a measure of dispersion.
Option D: 10
Option D (10) might result from incorrectly calculating the difference between consecutive values or making an arithmetic error in the subtraction.
High-Low Range Rule
Remember 'HI-LO = RANGE-O' - always subtract the LOwest value from the HIghest value to get the RANGE
How to use: When you see a range question, immediately identify the highest and lowest numbers in the data set, then use the HI-LO formula: Highest minus Lowest equals Range
Exam Tip
Always double-check that you're subtracting the smallest number from the largest number, not the other way around, as range must always be positive
Common Mistakes to Avoid
- -Confusing range with median (middle value)
- -Adding all values instead of finding the difference between extremes
- -Subtracting in the wrong order (low minus high instead of high minus low)
Concept Deep Dive
Analysis
Range is one of the fundamental measures of dispersion in statistics, representing the spread or variability within a data set. It provides a quick snapshot of how much the values differ from each other by measuring the distance between the extreme values. In real estate appraisal, understanding range helps appraisers assess the consistency and reliability of comparable sales data. A smaller range indicates more uniform data, while a larger range suggests greater variability that may require closer examination of the comparables.
Background Knowledge
Range is the simplest measure of variability in statistics, calculated as the difference between the maximum and minimum values in a data set. It's expressed in the same units as the original data and provides a basic understanding of data spread, though it can be heavily influenced by outliers.
Real-World Application
When analyzing comparable sales for a property appraisal, calculating the range of sale prices helps determine if the comparables are consistent enough to provide reliable value indicators, or if some sales should be excluded due to unusual circumstances
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