After taking six practice exams, Albert is reviewing his mistakes

Question

After taking six practice exams, Albert is reviewing the number of mistakes he made. On the first five exams, he made 7, 4, 8, 6 and 10 mistakes respectively.

In the table below, select a number of mistakes he could make on the 6th exam such that the mean number of mistakes is equal to the median number of mistakes. Then select a number of mistakes he could make on the 6th exam such that the mean (average) is greater than the median. Make only two selections, one in each column.

Kavicogsci · Answer

I believe you have to super quick in calculations with this one

But lets set some preparatory work first

Mistakes arranged in ascending order - 4,6,7,8,10

Sum of mistakes = 35

Let mistake for 6th exam be x

New mean after x = (35+x)/6

Now look at options for median - For first three options it is same (6+7)/2 = 6.5, four forth it is 7 and for last two option it is (7+8)/2 = 7.5

Now lets go one by one for each option

1. 1 -
Mean : (35+1)/6 = 6
Median : (6+7)/2 = 6.5
Nope - fits no case

2. 3
Mean : (35+3)/6 = ~6.3
Median : (6+7)/2 = 6.5
Nope - fits no case

3. 5 :
Mean: (35+5)/6 = 6.67
Median : (6+7)/2 = 6.5
Yes fits case were mean> median

4. 7
Mean : (35+3)/6 = 7
Median : 7

Fits case where both are equal

No need to do further

Only ans 7 and 5 fir our table

tgsankar10 · Answer

Mistakes arranged in order:  4, 6, 7, 8, 10  - Sum  =35  Mean  =7  Median  =7

Mean=Median=7

Case 1:    Mean=Median

7  mistakes made on the 6th exam will keep  Mean=Median

Case 2:    Mean>Median

whatever number be on the 6th exam, the median will be  6.5\leq{m}\leq{7.5}

if the mistakes are  >7 , the median will be  7.5

mistakes are  <7 , the median will be  6.5

mistakes are  =7 , the median will be  7

For  Mean>6.5 ,  6.5*6=39 , The 6th exam mistakes should be  >4

There is  5  in the options.

Answer: 7 & 5

Kinshook · Answer

@ariyanakAfter taking six practice exams, Albert is reviewing the number of mistakes he made. On the first five exams, he made 7, 4, 8, 6 and 10 mistakes respectively.

In the table below, select a number of mistakes he could make on the 6th exam such that the mean number of mistakes is equal to the median number of mistakes. Then select a number of mistakes he could make on the 6th exam such that the mean (average) is greater than the median. Make only two selections, one in each column.
Let the mistake made on the 6th exam be x.
Mistakes = {4,6,7,8,10,x} : x is unknown: Median number of mistakes = {7,(x+7)/2}: x is NOT greater than 7 since x is a positive integer.

Mean number of mistakes = (7+4+8+6+10+x)/6 = (35+x)/6

The number of mistakes he could make on the 6th exam such that the mean number of mistakes is equal to the median number of mistakes.
x = 7; Mean number of mistakes = 7 = Median number of mistakes

The number of mistakes he could make on the 6th exam such that the mean (average) is greater than the median.
(35+x)/6 > 6.5
x > 4; x = 5

Mean=Median  Mean > Median  
  7  5

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After taking six practice exams, Albert is reviewing his mistakes

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