George wrote seven tests and each was marked out of 100. No two of his marks were the same. He recorded the seven marks to do a statistical analysis. He accidentally recorded his highest mark higher than it actually was. How many of the following are altered because of his mistake?

- Mean
- Median
- Minimum test score
- Range
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Solution 1

Since George recorded his highest mark higher than it was, then if he writes his seven marks in order from lowest to highest, the order will not be affected.

So the minimum test mark is not affected, nor is the median test mark (which is the middle of the seven different marks).

Is either of the range or mean affected?

The range is difference between the highest mark and the lowest mark, so by recording the highest mark higher, the range has become larger.

The mean is the sum of the seven marks divided by 7 , so since the highest mark is higher, the sum of the 7 marks will be higher, and so the mean will be higher.

So only the mean and range are affected.

## Solution 2

Suppose that George's marks were $80,81,82,83,84,85$, and 86 , but that he wistfully recorded the 86 as 100 .

Originally, with marks $80,81,82,83,84,85,86$, the statistics are

Mean

Median

Minimum test score

Range

$$
\frac{80+81+82+83+84+85+86}{7}=83
$$

83

80

$86-80=6$

With marks $80,81,82,83,84,85,100$, the statistics are

Mean

Median

Minimum test score

Range

$$
\frac{80+81+82+83+84+85+100}{7}=85
$$

## 83

80

$100-80=20$

So the mean and range are the only statistics altered.

Answer: (C)