What is the first quartile , Q1,of the following distribution ? 24,26,26,27,28,31,33,35,37,38,40,42,43,46,48,55,56
2 answers:
Answer:
A. 27.5
Step-by-step explanation:
We have been given a data set. We are asked to find first quartile of our given data set.
24, 26, 26, 27, 28, 31, 33, 35, 37, 38, 40, 42, 43, 46, 48, 55, 56.
We can see that our given data set is in ascending form and it has 17 data points.
The median of the data set is 9th data point that is 37. The first quartile will be median of lower half.
The 1st quartile will be average of 4th and 5th data point that is:
Therefore, the first quartile of the given data set is 27.5 and option A is the correct choice.
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9514 1404 393
Answer:
D
Step-by-step explanation:
In the second quadrant, ...
c = 180° -arcsin(24/25) ≈ 106.26°
In the third quadrant, ...
d = 360° -arccos(-3/4) ≈ 221.41°
Then cos(c+d) = cos(327.67°) ≈ 0.84498
This is a positive irrational number, greater than 21/100, so the only reasonable choice is the last one:
_____
Perhaps you want to work this out using the trig identities.
cos(c) = -√(1 -sin(c)²) = -7/25
sin(d) = -√(1 -cos(d)²) = -(√7)/4
Then the desired cosine is ...
cos(c+d) = cos(c)cos(d) -sin(c)sin(d)
cos(c+d) = (-7/25)(-3/4) -(24/25)(-√7/4)
cos(c+d) = (21 +24√7)/100 . . . . matches choice D