Explain why the range must be above 40
Answers
Answer:
Step 1: Sort the numbers in order, from smallest to largest:
7, 10, 21, 33, 43, 45, 45, 65, 67, 87, 98, 99
Step 2: Subtract the smallest number in the set from the largest number in the set:
99 – 7 = 92
The range is 92
That’s it!
Example question 2: What is the range of these integers?
14, -12, 7, 0, -5, -8, 17, -11, 19
Step 1: Sort the numbers in order, from smallest to largest:
-12, -11, -8, -5, 0, 7, 14, 17, 19
Step 2: Subtract the smallest number in the set from the largest number in the set:
19 – -12 = 19 + 12 = 31
The range is 31.
That’s it!
Example question 3: What is the range of the following times?
2.7 hrs, 8.3 hrs, 3.5 hrs, 5.1 hrs, 4.9 hrs
Step 1: Sort the numbers in order, from smallest to largest:
2.7, 3.5, 4.9, 5.1, 8.3
Step 2: Subtract the smallest number in the set from the largest number in the set:
8.3 hr – 2.7 hr = 5.6 hr
The range is 5.6 hr.
That’s how to find a range!
Another Example.
Problem: You take 7 statistics tests over the course of a semester. You score 94, 88, 73, 84, 91, 87, and 79. What is the range of your scores?
Solution:
Step 1: Order your scores from smallest to largest:
73, 79, 84, 87, 88, 91, 94.
Step 2: Subtract the smallest number from the highest = 94 – 73 = 21.
Answer: 21.
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When it Might be Misleading
The range only uses the smallest and the largest number in a set; The rest of the values are ignored. That could lead to a misleading result. Take the above test scores. Let’s say you had the flu one test day and scored a 10. Assuming your highest score on another test was 94, then:
94 – 10 = 84!
That’s not a good reflection of your overall test performance at all.
The score of 10 in the example above is what we call an outlier. It’s an extremely high or low value that can throw off stats. That’s why other measures of spread are sometimes preferred, like the mean.
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Rule of Thumb
The rule of thumb says that the range is about four times the standard deviation. The standard deviation is another measure of spread in statistics. It tells you how your data is clustered around the mean. What the rule of thumb tells you in most cases is that the bulk of the data can be found pretty close to the mean (within a couple of standard deviations); The result is that those erroneous “outliers” should have very little effect on your final statistic.
Procedure for finding a standard deviation using the rule of thumb: