Statistics

IMO D

let x be the wrongly recorded sale

one of Cal's sales was incorrectly recorded as one of Ann's sales

so ann's total sale = 45000-x
and cal's sale =19000-x

given that median of all the sales = 330,000 and also
After the correction, Ann's total sales were still higher than Cal's total sales

=> median will be the ann's total sales

arranging the sales in increasing order will be 210,000,190,000+x,450000-x,360000,680000

=> 450000-x=330000
=>x =120000

ruchisharma wrote:Ann- 450,000
Bob- 360,000
Cal- 190,000
Dot- 210,000
Ed- 680,000

The data above shows the total sales in July recorded by 5 people. It was discovered that one of Cal's sales was incorrectly recorded as one of Ann's sales. After this error was corrected, Ann's total sales were still higher than Cal's total sales and the median of 5 sales was 330,000. What was the value of the incorrectly recorded sale?

a) 30,000
b) 48,000
c) 90,000
d) 120,000
e) 140,000

This is a perfect problem for plugging in the answer choices, which represent the number of sales we need to take from Ann and give to Cal.

Answer choice C:
New Ann = 450,000 - 90,000 = 360,000
New Cal = 190,000 + 90,000 = 280,000
New sales list from smallest to biggest: 210,000; 280,000; 360,000; 360,000; 680,000.
Median = 360,000. Doesn't work. We need to take more from Ann.

Answer choice D:
New Ann = 450,000 - 120,000 = 330,000
New Cal = 190,000 + 120,000 = 310,000
New sales list from smallest to biggest: 210,000; 310,000; 330,000; 360,000; 680,000.
Median = 330,000. Success!

The correct answer is D.

ruchisharma wrote:Ann- 450,000
Bob- 360,000
Cal- 190,000
Dot- 210,000
Ed- 680,000

The data above shows the total sales in July recorded by 5 people. It was discovered that one of Cal's sales was incorrectly recorded as one of Ann's sales. After this error was corrected, Ann's total sales were still higher than Cal's total sales and the median of 5 sales was 330,000. What was the value of the incorrectly recorded sale?

a) 30,000
b) 48,000
c) 90,000
d) 120,000
e) 140,000

We can also solve this via logic/common sense.

Median represent the middle term of a list with an odd number of items. Since we have 5 people, the median will be the term right in the middle.

So, there have to be 2 people below 330k, 1 person right at 330k and 2 people above 330k.

Currently, there are 2 people below 330k and 3 people above 330k. Therefore, we need to adjust someone down to get the distribution that we want.

Since we can only adjust Ann and Cal, and since Cal is currently below 330k, Ann must be the person we're adjusting. To get Ann from 450k to 330k, we must deduct 120k... choose (D)!