What is the IQR of 15,19,20,25,25,28,29,30,30,35,37,43
2 answers:
Answer:
IQR = 10
Step-by-step explanation:
The interquartile range is the difference between the upper quartile and the lower quartile.
Firstly find the median of the data set.
The median is the middle value of the data arranged in ascending order. If there is no exact middle then it is the average of the 2 values either side of the middle.
15 19 20 25 25 28 29 30 30 35 37 43
↑median
median = = 28.5
The lower quartile is the middle of the data to the left of the median.
15 19 20 25 25 28
↑ lower quartile
lower quartile = = 22.5
The upper quartile is the middle of the data to the right of the median
29 30 30 35 37 43
↑ upper quartile
upper quartile = = 32.5
IQR = 32.5 - 22.5 = 10
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looking at the picture, the interior angles are not right-angles, and thus is not a rectangle, and is not a square either, due to the same reason
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now, we don't need to check the length of both pairs, just one of the segments of each pair, let's check only then JK and KL, the ones in red in the picture, since each pair of segments are twin, if JK = KL, then that means all sides are equal
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now... another characteristic of a rhombus is, the diagonals, meet at right-angle, that means KM ⟂ JL
and that simply means, if you get the slope of KM and the slope of JL, the product of their slope is -1
then multiply both slopes, if their product is -1, that means, they're perpendicular to each other, and it IS a rhombus only, then.
now, we know is a parallelogram, so the diagonals will bisect
looking at the picture, the interior angles are not right-angles, and thus is not a rectangle, and is not a square either, due to the same reason
is it a rhombus? well, a rhombus, is a parallelogram, that's "slanted" per se, but regardless of how slanted it may be, the sides are all equal
now, we don't need to check the length of both pairs, just one of the segments of each pair, let's check only then JK and KL, the ones in red in the picture, since each pair of segments are twin, if JK = KL, then that means all sides are equal
now... another characteristic of a rhombus is, the diagonals, meet at right-angle, that means KM ⟂ JL
and that simply means, if you get the slope of KM and the slope of JL, the product of their slope is -1
then multiply both slopes, if their product is -1, that means, they're perpendicular to each other, and it IS a rhombus only, then.
