Which box-and-whisker plot represents the data set? 11, 6, 19, 14, 21, 7, 13, 15, 15
1 answer:
The box and whisker plot is attached.
We first order the data from least to greatest:
6, 7, 11, 13, 14, 15, 15, 19, 21
The median is the middle value, or 14.
The lower quartile is the median of the lower half (split by the median). This is between 7 and 11: (7+11)/2 = 18/2 = 9
The upper quartile is the median of the upper half (split by the median). This is between 15 and 19: (15+19)/2 = 34/2 = 17
The highest value is 21.
The lowest value is 6.
We draw the middle line of the box at 14, the median. We draw the left side of the box at the lower quartile, 9. We draw the right side of the box at the upper quartile, 17. From the right side of the box, we draw a whisker to the highest value, 21. From the left side of the box, we draw a whisker to the lowest value, 6.
We first order the data from least to greatest:
6, 7, 11, 13, 14, 15, 15, 19, 21
The median is the middle value, or 14.
The lower quartile is the median of the lower half (split by the median). This is between 7 and 11: (7+11)/2 = 18/2 = 9
The upper quartile is the median of the upper half (split by the median). This is between 15 and 19: (15+19)/2 = 34/2 = 17
The highest value is 21.
The lowest value is 6.
We draw the middle line of the box at 14, the median. We draw the left side of the box at the lower quartile, 9. We draw the right side of the box at the upper quartile, 17. From the right side of the box, we draw a whisker to the highest value, 21. From the left side of the box, we draw a whisker to the lowest value, 6.
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A conditional statement involves 2 propositions, p and q. The conditional statement, is a proposition which we write as: p⇒q,
and read "if p then q"
Let p be the proposition: Triangle ABC is a right triangle with m(C)=90°.
Let q be the proposition: The sides of triangle ABC are such that
.
An example of a conditional statement is : p⇒q, that is:
if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that
This compound proposition (compound because we formed it using 2 other propositions) is true. So the truth value is True,
the converse, inverse and contrapositive of p⇒q are defined as follows:
converse: q⇒p
inverse: ¬p⇒¬q (if [not p] then [not q])
contrapositive: ¬q⇒¬p
Converse of our statement:
if The sides of triangle ABC are such that
then Triangle ABC is a right triangle with m(C)=90°
True
Inverse of the statement:
if Triangle ABC is not a right triangle with m(C) not =90° then The sides of triangle ABC are not such that
True
Contrapositive statement:
if The sides of triangle ABC are not such that then Triangle ABC is not a right triangle with m(C)=90°
True
and read "if p then q"
Let p be the proposition: Triangle ABC is a right triangle with m(C)=90°.
Let q be the proposition: The sides of triangle ABC are such that
An example of a conditional statement is : p⇒q, that is:
if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that
This compound proposition (compound because we formed it using 2 other propositions) is true. So the truth value is True,
the converse, inverse and contrapositive of p⇒q are defined as follows:
converse: q⇒p
inverse: ¬p⇒¬q (if [not p] then [not q])
contrapositive: ¬q⇒¬p
Converse of our statement:
if The sides of triangle ABC are such that
then Triangle ABC is a right triangle with m(C)=90°
True
Inverse of the statement:
if Triangle ABC is not a right triangle with m(C) not =90° then The sides of triangle ABC are not such that
True
Contrapositive statement:
if The sides of triangle ABC are not such that
True