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The table above shows the distribution of scores on a geography quiz

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Re: The table above shows the distribution of scores on a geography quiz [#permalink]
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hmazariegos wrote:

The table above shows the distribution of scores on a geography quiz given to a class of 25 students. Which of the following is closest to the average (arithmetic mean) quiz score for the class?

A. 8.6
B. 8.5
C. 8.4
D. 8.3
E. 8.0

Attachment:
gmat quiz question.JPG

Using the weighted average formula, we have:

(6 x 2 + 7 x 4 + 8 x 7 + 9 x 9 + 10 x 3)/25

(12 + 28 + 56 + 81 + 30)/25

207/25 = 8.28, which is about 8.3.

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Re: The table above shows the distribution of scores on a geography quiz [#permalink]
hmazariegos wrote:

The table above shows the distribution of scores on a geography quiz given to a class of 25 students. Which of the following is closest to the average (arithmetic mean) quiz score for the class?

A. 8.6
B. 8.5
C. 8.4
D. 8.3
E. 8.0

Attachment:
gmat quiz question.JPG

$$\frac{6*2+7*4+8*7+9*9+10*3}{25} = 8.28 = 8.30$$, Answer must be (D)
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Re: The table above shows the distribution of scores on a geography quiz [#permalink]
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Sabby Bunuel

Wanted to understand that this base point method is valid for all no. or even spaced list.
If list is not evenly spaced, how to consider base point?

Sabby wrote:
I always use the base point method to avoid big calculation and therefore get the result under 1 minute:

First, without weighted average, the AVG is 8 : (first term+last term)/2 = (6+10)/2 = 8

Now let's take the AVG 8 as our base point:

Scores from base point 8 : 6 is -2 from base point, 7 is -1, 9 is +1 and 10 is +2

Finally, let's proceed to calculate the weighted average:
-2*(2/25)-1*(4/25)+1*(9/25)+2*(3/25) = -4/45-4/25+9/25+6/25=7/25=28/100 or 0.28

Add the result to the basepoint : 8+0.28= 8.28

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Re: The table above shows the distribution of scores on a geography quiz [#permalink]
Sneha2021 wrote:
Sabby Bunuel

Wanted to understand that this base point method is valid for all no. or even spaced list.
If list is not evenly spaced, how to consider base point?

Sabby wrote:
I always use the base point method to avoid big calculation and therefore get the result under 1 minute:

First, without weighted average, the AVG is 8 : (first term+last term)/2 = (6+10)/2 = 8

Now let's take the AVG 8 as our base point:

Scores from base point 8 : 6 is -2 from base point, 7 is -1, 9 is +1 and 10 is +2

Finally, let's proceed to calculate the weighted average:
-2*(2/25)-1*(4/25)+1*(9/25)+2*(3/25) = -4/45-4/25+9/25+6/25=7/25=28/100 or 0.28

Add the result to the basepoint : 8+0.28= 8.28

Hi Sneha2021

You can take any base point and can use this concept no matter how evenly spaced the sequence is

Let's consider an example with different scores that are not evenly spaced but with the same number of students : 6 7 13 20 22
Now let's say we choose 13 as the basepoint

-7*(2/25) + -6*(4/25)+0*(7/25)+ 7*(9/25)+ 9*(3/25)
= (-14-24+63+27)/25
= 52/25
= 2+0.08 or 2.08

The weighted average is 13+2.08= 15.08

Let me know whether this helps or not

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Re: The table above shows the distribution of scores on a geography quiz [#permalink]
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Re: The table above shows the distribution of scores on a geography quiz [#permalink]
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