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How many numbers less than median?

Posted on 2011-09-25
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A survey of the cost of one-pound bags of potato chips at five local supermarkets is shown in the attached stem-and-leaf plot.  How many bags of chips cost less than the median price of a bag of chips?

Key of stem-and_leaf plot is as follows:

  15 | 9 means $1.59

Our solution:  $1.59, $1.69, $1.75, $1.79, $1.88, $1.89, $1.99, $1.99, $1.99, $1.99, $1.99, $2.09, $2.15, $2.15, $2.18, $2.19, $2.25, $2.29, $2.29, $2.39, $2.40, $2.59

Median = ($1.99 + $2.09)/2 = $2.04

but our answer doesn't come out to be 6. stem-and-leaf plot
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Question by:naseeam
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by:aburr
ID: 36596219
If your answer was not 6, what was it?
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by:naseeam
ID: 36596225
Our answer is 11 because 11 bags of chips cost less than median price $2.04.
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by:aburr
ID: 36596250
I think the difficulty may be in the definition of "medium". Thus I would tend to agree with your answer above
BUT
you have a leaf diagram and the middle of it is 6 items above the bottom. (The real middle is at 5.5 as per your calculation but that rounds to 6
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by:PaulHews
ID: 36596278
2.40 is not a data point, thus the median is 1.99, thus there are 6 points lower than the median.
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by:Paul Sauvé
ID: 36596281
Please see this article on HOW to find the "median value".
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by:naseeam
ID: 36596291
Why 2.40 is not a data point?
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by:aburr
ID: 36596337
There is no number in your collection of date points which equals 2.04
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by:TommySzalapski
ID: 36596384
So there are 11 bags of chips that are less than the median, but 6 prices that are less than the median chip bag price.
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by:naseeam
ID: 36596451
>> So there are 11 bags of chips that are less than the median, but 6 prices that are less than the median chip bag price.

Since $1.99 is one of two median numbers, should it be counted as one of 6 prices?  If it's counted, then there are 7 prices less than median price.
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PaulHews earned 500 total points
ID: 36596658
>Why 2.40 is not a data point?

24 has no leaves... Empty stem, with no data.  If it were meant to be 2.40 you would see 24|0

>Since $1.99 is one of two median numbers, should it be counted as one of 6 prices?  If it's counted, then there are 7 prices less than median price.

When there are an even number of points you take the mean of the two middle points as you showed in the text of the question and derive a single median.  However there is an odd number of points (21), so 1.99 is the median number we need to consider.

The question "How many bags of chips cost less than the median price of a bag of chips?" indicates not the number of points before the median, but the number of data points that are less than the median.  There are exactly six ($1.59, $1.69, $1.75, $1.79, $1.88, $1.89)

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