Isabella and three of her friends were comparing their typing speeds

Question

Isabella and three of her friends were comparing their typing speeds as measured by an online typing test. The average (arithmetic mean) of the 4 speeds was 45 words per minute (wpm), the range of the 4 speeds was 40 wpm, and the median of the 4 speeds was equal to Isabella's speed.

In a manner that is jointly consistent with the given information, select for Slowest a speed that could be the slowest of the 4 speeds, in wpm, and select for Median a value that could be the median of the 4 speeds, in wpm. Make only two selections, one in each column.

AndrewN · Accepted Answer

Hello,  sallyabdul . Thank you for posting this question, one that is more mathematical than some IR questions. To get to the bottom of the matter (and to avoid feeling overwhelmed), it can help to pause at each punctuation mark to assess what information you have.

- Sentence one tells us that there are  four people  involved.

- Sentence two branches in three directions, but you can easily separate the information by the commas:   The average speed was 45 wpm   The range of speeds, or the difference between the fastest and slowest speeds, was 40 wpm   Isabella typed at the same speed as the median speed

Work through one bullet point at a time:

1) If the average speed was 45 wpm, then the sum of the word count of the four typists was 45 * 4, or 180 words. Remember, average equals a sum divided by the number of items being counted, and here, we are only missing that sum.

2) Since the average was 45 wpm, and we know from the second bullet point that the range of values was 40, it seems reasonable to test a value lower than 45 for the slowest speed. How about 25? This would mean that the highest value would be restricted to 65 (from 25 + 40). As long as the two other values between 25 and 65 could be added in such that the sum of the four numbers was 180, we would be fine.

25+x+y+65=180

x+y+90=180

x+y=90

We can appreciate that two values between 25 and 65 would, in fact, add up to 90, so 25 seems probable for our slowest speed. We just have to check everything against the third bullet point.

3) If Isabella typed the same speed as the median speed, since we know we are dealing with an even-numbered set of speeds—four—the median value will be the average of the two middle values. The only way, then, for Isabella to have typed the median speed is if she had typed 45 wpm, the same as one of her friends. Thus, we can deduce that  x  and  y  above from step 2) would be 45 and 45 (the average of which would be 45, of course).

Final answer:

Slowest  
  Median   
   
    √      25  
      30  
      √    45  
      50  
      55  
      60

I hope that helps. Good luck with your studies.

- Andrew

jhavyom · Answer

Isabella and three of her friends were comparing their typing speeds as measured by an online typing test. The average (arithmetic mean) of the 4 speeds was 45 words per minute (wpm), the range of the 4 speeds was 40 wpm, and the median of the 4 speeds was equal to Isabella's speed.

Let Isabella's three friends be A, B, and C.
Let their speeds in wpm be I, A, B, and C respectively.
Let their typing speeds in the increasing orders be A, B, I, and C.
A>B>I>C

For 4 numbers, the avg. of the middle two numbers is a median.
Since I is a median. B must be equal to I.
So, A>B=I>C

Also, the average of A, B, I, and C is 45
or, (A+B+I+C)/4 = 45
(A+B+I+C) = 180

Since, range = 40
A = C + 40
  = 180
2C + 2I + 40 = 180
C + I = 70

Here, C is the slowest and I is the median.

From the given options, C can be only 25 or 30 (it has to be less than the average i. e. 45)

Check for C = 25
I = 70 - 25 = 45 = Median 
This matches with the given options

Check for C = 30
I = 70 - 30 = 40 = Median
40 is not in the list.

So, the answer is 
slowest = 25
median = 45

Dare Devil · Answer

Isabella and three of her friends were comparing their typing speeds as measured by an online typing test. The average (arithmetic mean) of the 4 speeds was 45 words per minute (wpm), the range of the 4 speeds was 40 wpm, and the median of the 4 speeds was equal to Isabella's speed.

Median:

Median of 4 numbers = Average of 2nd and 3rd number
Average of 2 different numbers will fall in between them, but given median is equal to Isabella's speed. This is only possible when two are equal
=> 2nd = 3rd = 45 in turn median = 45

Slowest:
Given Range => Max-Min = 40
Ley 'y' be the slowest and 'x' be Fastest => y-x = 40

Given Average of 4 numbers = 45
(y+x+45+45)/4 = 45 (From Median calculations two numbers are 45) 
Solving x+y = 90

From Equations 1 and 2
y-x = 40
y+x = 90

y = 25, x = 65

Slowest = 25

GOYA1025 · Answer

Order by slowest to fastest: X, A, B, X+40

Since (A+B)/2=M, A+B=2M

So, X+2M+X+40=180, them X+M=70

X=25 and M=45

bumpbot · Answer

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Isabella and three of her friends were comparing their typing speeds

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