SOLUTION: A researcher was recording the amount ,(in centimeters), the root system for a new variety of plant was growing during a 6 week period. A sample of 10 plants had the following leng

Question 1110538: A researcher was recording the amount ,(in centimeters), the root system for a new variety of plant was growing during a 6 week period. A sample of 10 plants had the following lengths:
2 . 5, 3, 2 . 7, 1.5, 2, 3.2, 4, 4.3, 1.7, 4.1
What is the length that corresponds to the 25th percentile?

a. 1.7

b. 2

c. 3.2

d. 4.3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

The answer is choice B) 2

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Explanation:

Given Data Set = {2.5, 3, 2.7, 1.5, 2, 3.2, 4, 4.3, 1.7, 4.1}
Sorted Data Set = {1.5, 1.7, 2, 2.5, 2.7, 3, 3.2, 4, 4.1, 4.3}

I'm going to mark the middle most values in red of the sorted set
{1.5, 1.7, 2, 2.5, 2.7, 3, 3.2, 4, 4.1, 4.3}
The middle values happen to be two values as there are an even number of items in this set
The median is the midpoint of 2.7 and 3.
The median is 2.85.
We find this by averaging 2.7 and 3. So add them up and divide by 2: (2.7+3)/2 = 5.7/2 = 2.85

Now break the sorted list into two halves. The lower half looks like
L = {1.5, 1.7, 2, 2.5, 2.7}
and the upper half is
U = {3, 3.2, 4, 4.1, 4.3}

The lower half of values L = {1.5, 1.7, 2, 2.5, 2.7} are all below the median 2.85

Locate the median of list L. The middle most value here is 2.
So the first quartile is 2. This is the value of the 25th percentile which coincides with the first quartile (Q1).

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