Probability using box and whisker

In summary, the conversation discusses the process of finding the probability that two salmon, randomly selected from a group of 39 with no repeated lengths, will both be longer than the lower quartile value. The solution involves determining the number of lengths above the lower quartile and adjusting for the second pick to get a final probability of 54.8%. However, it is also suggested that using the estimate of 56.3% may also be a reasonable approach. The question of which solution is preferred for a standardized test is also raised.
  • #1
joel amos
104
0
The question:
A box and whisker plot is made from the lengths of 39 salmon. No two lengths are the same. Two of the salmon are picked at random. What is the probability that they will both be longer than the lower quartile value.

My solution:
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

The x's stand for the 39 lengths. The underlined ones are (respectively) the minimum, lower quartile, median, upper quartile, and maximum. There are 29 x's above the lower quartile value (including the second x that was averaged to find that value). Therefore, the probability for the first pick would be 29/39. For the second pick, however, the quantities have been lowered by one since one salmon has already been picked. So the second probability is 28/38. When multiplied together, I got a final probability of 54.8% Is this correct, or am I somehow over-complicating the problem. What would you give as the answer?
 
Physics news on Phys.org
  • #2
I would do the same.

If 1-2% do not matter, 0.75^2 = 56.3% gives a reasonable estimate.
 
  • #3
Yeah, that's what a lot of people did. This was a standardized test open-ended question. I wonder which response they're looking for.
 

What is a box and whisker plot?

A box and whisker plot is a graphical representation of numerical data that shows the distribution of the data, including the median, quartiles, and outliers.

How do you create a box and whisker plot?

To create a box and whisker plot, first find the median, upper and lower quartiles, and any outliers in the data set. Then, draw a number line and mark the minimum and maximum values. Next, draw a box that extends from the lower quartile to the upper quartile, with a line at the median. Finally, draw lines (whiskers) extending from the box to the minimum and maximum values, with any outliers represented as dots or crosses.

What information can be determined from a box and whisker plot?

A box and whisker plot can provide information about the center, spread, and shape of a data set. The median represents the center, while the distance between the upper and lower quartiles shows the spread. The shape of the plot can indicate if the data is symmetrical or skewed, and any outliers can also be identified.

How is probability used in box and whisker plots?

Probability can be used in box and whisker plots to determine the likelihood of a data point falling within a certain range. For example, the probability of a data point falling within one standard deviation of the mean is approximately 68%.

What are the advantages of using a box and whisker plot?

Box and whisker plots provide a visual representation of data that is easy to interpret and compare between different data sets. They also show the distribution of the data and any outliers, making it easier to identify patterns and make inferences about the data.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
4K
  • Programming and Computer Science
Replies
1
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
8
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
19
Views
11K
  • Special and General Relativity
Replies
5
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
Back
Top