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15 items of clothing were purchased from store S
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Updated on: 02 Aug 2022, 03:10
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Question Stats:
50% (01:19) correct
50% (00:14) wrong based on 2 sessions
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15 items of clothing were purchased from store S. The average (arithmetic mean) sale price of the items was $140 and the median sale price was $120.
Quantity A
Quantity B
The minimum price at which the most expensive item could be purchased
$155
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
Originally posted by thetombs98 on 01 Aug 2022, 17:13.
Last edited by Carcass on 02 Aug 2022, 03:10, edited 1 time in total.
15 items of clothing were purchased from store S
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03 Aug 2022, 04:38
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Theory
➡ Average = Sum of all the Values / Total Number of Values ➡ Sum of All the values = Average * Total Number of Values ➡ Median is the middle value of the set (after arranging the set in ascending or descending order)
Given that Average = $140 and Median price is $120 and there are 15 items which are purchased. Since, median is $120 and there are odd number of values (15) so middle term, which is the \(8^{th}\) term, will be the median. => \(8^{th}\) term = Median = $120
Quantity A
The minimum price at which the most expensive item could be purchased
Now, for the maximum price to be minimum
➡ All the values greater than median should be equal and should be least ➡ All the values less than median should be equal and should be greatest => should be equal to Median
=> First 7 values = Median = $120 => Sum of First 7 values = 7*$120 = $840
Last Seven values are equal, let each values is x => Sum of last 7 values = 7x
Total Sum = Average * 15 = $140*15 = $2100 => Sum of First 7 values + $120 + Sum of last 7 values = $2100 => $840 + $120 + 7x = $2100 => 7x = $2100 - $960 = $1140 => x = \(\frac{$1140}{7}\) ~ $162 => Minimum value of Maximum purchase price = $162
=> Quantity A ($162) > Quantity B($155)
So, Answer will be A. Hope it helps!
Watch the following video to Learn the Basics of Statistics