Question 252330: Please help me solve this problem: In an exercise gym, 5 different people used a particular weight-training machine.
Name Weight
Mona 40
Sam 80
Tony 80
Alba 60
Peter 110
Use the data above to find the mean, median, mode. and range of the data. What effects does multiplication by a fixed number have on the mean, median, mode, and range of the data? Explain the reasoning for your answer.
- I already found the mean, median, mode, and range.
mean=74
median=80
mode=80
range=70
I just DON'T GET the question about the fixed number... PLEASE HELP ME AND EXPLAIN!!!
-thankyou! :)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let k = some fixed number (ie a constant). In other words, k is some number (we just don't know what it is).
Now multiply EVERY data value by k to get:
Mona 40k
Sam 80k
Tony 80k
Alba 60k
Peter 110k
Now let's find the following:
Mean: Add up the values and divide by 5 (the number of people there) to get
So the mean of the data values of 40k, 80k, 80k, 60k, and 110k is 74k. What this means is that the mean is just the original mean multiplied by the constant k. So if k=2, then the new mean is 2*74=148
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Median: First write the values in ascending order:
40, 60, 80, 80, 110
Now multiply each value by k:
40k, 60k, 80k, 80k, 110k
From this list, the middle most value is 80k. Since the original median is 80, the new median is just the result of multiplying the original median of 80 by the constant k. I bet you can guess what's going to happen with the mode and the range.
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Mode:
Looking at the list
40k, 60k, 80k, 80k, 110k
we see that the mode is 80k since 80k repeats itself twice and it is the most frequent number. Because the original mode is 80, the new mode is just the product of the old mode and k.
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Range:
The range of the list
40k, 60k, 80k, 80k, 110k
is just the difference between the largest element (110k) and the smallest element (40k). In other words the range is: 110k - 40k = 70k which is exactly the product of the original range and the constant k.
So multiplying every element in a data set by a fixed number will just multiply the mean, median, mode, and range by that same fixed number. Try picking some specific numbers (like k=2, k=3, etc) to give you some examples.
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