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Lunna [17]
3 years ago
14

Find the median, first quartile, third quartile, interquartile range, and any outliers for each set of data.

Mathematics
2 answers:
larisa86 [58]3 years ago
5 0

Answer:

First, to find the median, we have to order all numbers, from least to highest:

<h3>2.8; 3.9; 5.3; 6.1; 6.5; 7.1; 12.5; 14.6; 16.4; 16.4; 20.8; 27.1; 28.1; 30.9; 53.5</h3>

Now, we calculate the position of each quartile:

Q_{k}=\frac{k(n+1)}{4}\\Q_{1}=\frac{1(15+1)}{4}=4\\Q_{2}=\frac{2(15+1)}{4}=8\\Q_{3}=\frac{3(15+1)}{4}=12

So, the first quartile is in the fourth position, the thirds quartile is in the twelfth position:

So, first quartile is 6.1. Second quartile is 14.6, and the third quartile is 27.1.

It's important to remember that the second quartile is the median. So the median is 14.6

Lastly, the interquartile range is the difference between the third and first quartile. So:

Q_{3}-Q_{1}=27.1-6.1=21

Therefore, the interquartile range is 21.

nadezda [96]3 years ago
3 0

Here is what i figured out.

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During the first hour of operation the farm stand owner sold 15% of the apples he had. On the second hour he sold 20% of the rem
liraira [26]

Answer:

 3.825 kg apples.

Step-by-step explanation:

Let x kg be the amount of apples stand owner had initially.

We have been given that during the first hour of operation the farm stand owner sold 15% of the apples he had. Then the amount of sold apples will be:

\text{The amount of sold apples during 1st hour}=\frac{15}{100}x=0.15x

\text{The amount of remaining apples after 1st hour}=x-0.15x

\text{The amount of remaining apples after 1st hour}=0.85x

On the second hour he sold 20% of the remaining apples. So the amount of sold apples on the second hour will be 20% of 0.85x.

\text{The amount of sold apples during 2nd hour}=0.85x*\frac{20}{100}  

\text{The amount of sold apples during 2nd hour}=0.85x\times 0.20  

\text{The amount of sold apples during 2nd hour}=0.17x

During the second hour 25.5 kg of apples were sold, so we can set up an equation as:

25.5=0.17x

\frac{25.5}{0.17}=\frac{0.17x}{0.17}

150=x

So, stand owner had initially 150 kg of apples.

\text{The amount of remaining apples after 2nd hour}=0.85x-0.17x

\text{The amount of remaining apples after 2nd hour}=0.68x

On the third hour he sold 25% of the remaining apples. So the amount of sold apples on the 3rd hour will be 25% of 0.68x

\text{The amount of sold apples during 3rd hour}=0.68x*\frac{25}{100}

\text{The amount of sold apples during 3rd hour}=0.68x*0.25

\text{The amount of sold apples during 3rd hour}=0.17x  

\text{The amount of remaining apples after 3rd hour}=0.68x-0.17x

\text{The amount of remaining apples after 3rd hour}=0.51x

As remaining apples were sold 5% more each following hour.

\text{The amount of sold apples during 4th hour}=0.51x*\frac{5}{100}

\text{The amount of sold apples during 4th hour}=0.51x*0.05

\text{The amount of sold apples during 4th hour}=0.0255x

Let us substitute x=150 into above equation we will get,

\text{The amount of sold apples during 4th hour}=0.0255*150

\text{The amount of sold apples during 4th hour}=3.825

Therefore, 3.825 kg of apples were sold during the 4th hour.

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Consider the given parallelogram KLMN.

Prove: \angle N \cong \angle L, \angle K \cong \angle M

 Statement                                                                       Reason

1. KL \parallel NM, KN \parallel LM               Definition of parallelogram

2. \angle K+ \angle N = 180^\circ                 Same Side interior angle theorem

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3. \angle K+ \angle N=\angle K+ \angle L   Substitution property

  \angle L+ \angle M=\angle K+ \angle L

4. \angle N = \angle L                                 Subtraction property of equality

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Subtraction property of equality tells us that if we subtract some number from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same.

5.  \angle N \cong \angle L                         Angle Congruence Postulate

  \angle M \cong \angle K

When two angles are equal, then they are said to be congruent by Angle congruence postulate.

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Answer:

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Step-by-step explanation:

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