Solved

How many numbers less than median?

Posted on 2011-09-25
10
434 Views
Last Modified: 2012-05-12
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
0
Comment
Question by:naseeam
  • 3
  • 3
  • 2
  • +2
10 Comments
 
LVL 27

Expert Comment

by:aburr
ID: 36596219
If your answer was not 6, what was it?
0
 
LVL 1

Author Comment

by:naseeam
ID: 36596225
Our answer is 11 because 11 bags of chips cost less than median price $2.04.
0
 
LVL 27

Expert Comment

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
0
Live: Real-Time Solutions, Start Here

Receive instant 1:1 support from technology experts, using our real-time conversation and whiteboard interface. Your first 5 minutes are always free.

 
LVL 38

Expert Comment

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.
0
 
LVL 31

Expert Comment

by:Paul Sauvé
ID: 36596281
Please see this article on HOW to find the "median value".
0
 
LVL 1

Author Comment

by:naseeam
ID: 36596291
Why 2.40 is not a data point?
0
 
LVL 27

Expert Comment

by:aburr
ID: 36596337
There is no number in your collection of date points which equals 2.04
0
 
LVL 37

Expert Comment

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.
0
 
LVL 1

Author Comment

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.
0
 
LVL 38

Accepted Solution

by:
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)

0

Featured Post

Courses: Start Training Online With Pros, Today

Brush up on the basics or master the advanced techniques required to earn essential industry certifications, with Courses. Enroll in a course and start learning today. Training topics range from Android App Dev to the Xen Virtualization Platform.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
Discrete Values 2 50
Binomial distribution 2 55
Permutation and Combination 9 85
Geomentry-Fundamental concepts 6 66
Have you ever thought of installing a power system that generates solar electricity to power your house? Some may say yes, while others may tell me no. But have you noticed that people around you are now considering installing such systems in their …
We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…

813 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question

Need Help in Real-Time?

Connect with top rated Experts

8 Experts available now in Live!

Get 1:1 Help Now