The range for a set of measurements is 24.7. If 6 were added to each

Question

﻿The range for a set of measurements is 24.7. If 6 were added to each measurement and then each of the adjusted measurements were divided by 10, what would be the range of the final set of measurements?

A. 30.70
B. 25.20
C. 24.70
D. 3.07
E. 2.47

JeffTargetTestPrep · Accepted Answer

If we add the same constant to each element of any data set, then the range of the values in the new data set will be equal to the  original range .

On the other hand, if we divide each element of any data set by the same nonzero constant, then the range of the values in the new data set will be equal to the  original range divided by the absolute value of the same constant .

original range = 24.7

new range = (24.7)/10 = 2.47

Answer: E

Note: If you don’t know the above rules, then a good strategy to solve such a problem is to select some valid values that satisfy all constraints and then make the calculations with the selected values.

For example:

set₁ = {0, 24.7}  
set₂ = {6, 30.7} [Divide each element by 10.}
set₃ = {0.6, 3.07}

new range = 3.07 – 0.6 = 2.47

gmatophobia · Answer

The addition of a constant term doesn't affect the range. Hence, if 6 were added to each measurement the range would still be 24.70.

However, when each of the adjusted measurements is divided by 10, the range of the set gets divided by the absolute value of the factor, i.e. 10 in this case.

Final Range =  \frac{24.70 }{ 10} = 2.47

Option E

spy2206 · Answer

So, can we say that standard deviation and range rules similar when it comes to adding/subtrating and multiplying/dividing constant to each element in a set? JeffTargetTestPrep

KarishmaB · Answer

Visualize the set on the number line. If 6 is added to each number, the entire set just moves ahead by 6 units. 
Now when each measurement is divided by 10, it becomes a tenth of its previous value so the entire set contracts to a tenth of its value. The smallest and the largest numbers stay smallest and largest respectively but both become a tenth of their previous value. So their difference also becomes a tenth of its previous value. Hence range becomes 24.7/10 = 2.47

Answer (E)

Take an example to see this in action:
Initial Measurements are 1, 4, ... 25.7.
Range = 25.7 - 1 = 24.7

Add 6 to each: 7, 10, ... 31.7. 
Range = 31.7 - 7 = 24.7

Divide each by 10: 7/10, 1/10, ... 31.7/10.
 Range = \frac{1}{10} (31.7 - 7) = \frac{1}{10} * 24.7 = 2.47

Spacepanda · Answer

imagine a number line
that consists of values from 0 to 24.7
Range of this line is (highest-lowest)= 24.7
now if we add 6 to all elements in this range, then
lowest=0+6 =6
highest=24.7+6 =30.7
now adjusted measurements were divided by 10
lowest=0.6
highest=3.07
therefore range= 3.07-6 = 2.47

Dbrunik · Answer

i see a lot of words above, and i think the best way to think about this is actually with a number line

bumpbot · Answer

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The range for a set of measurements is 24.7. If 6 were added to each

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The range for a set of measurements is 24.7. If 6 were added to each

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