What is the interquartile range of the data set? {33, 38, 45, 56, 57, 63, 72, 91}

2 answers
Question:

What is the interquartile range of the data set? {33, 38, 45, 56, 57, 63, 72, 91}

Answers

The IQR = 26.
The interquartile range (IQR) is found by subtracting the first quartile from the third quartile (Q3 - Q1 = IQR).

First Quartile (Q1) = 41.5
To find the first quartile, you find the middle value between the minimum value of the set and the set's median. The minimum value of the set is 33, and the median is 56.5 (56 + 57 = 113, 113/2 = 56.5).

Since there are an even number of values in the set, split it in half. Find the median in the lesser half of values: {33, 38, 45, 56}. The two middle values are 38 and 45, which you add together and divide by 2 to get the first quartile. 33 + 38 = 83, 83/2 = 41.5

Third Quartile (Q3) = 67.5
The second half of the data values from when you split the set in half earlier is composed of the numbers {57, 63, 72, 91}. Add 63 and 72 together to get 135 and divide by 2 to find the 3rd Quartile value. 135/2 = 67.5

Interquartile Range: 26
The IQR is found by subtracting Q3 - Q1. You get 67.5 - 41.5 which equals 26. The IQR is 26.

[tex]IQR =Q_3 -Q_1[/tex]

We have for this case n= 8 values. In order to find the Q1 we can select the first 4 values {33, 38, 45, 56 and the Q1 would be:

[tex]Q_1 = \frac{38+45}{2}= 41.5[/tex]

And for the Q3 we can select the last 4 values 57, 63, 72, 91 and for Q3 we got:

[tex]Q_3= \frac{63+72}{2}= 67.5[/tex]

And then the interquartile range would be:

[tex]IQR =Q_3 -Q_1 = 67.5-41.5 = 26[/tex]

Step-by-step explanation:

For this problem we have the following dataset ordered:

{33, 38, 45, 56, 57, 63, 72, 91}

And we want to find the interquartile range defined as:

[tex]IQR =Q_3 -Q_1[/tex]

We have for this case n= 8 values. In order to find the Q1 we can select the first 4 values {33, 38, 45, 56 and the Q1 would be:

[tex]Q_1 = \frac{38+45}{2}= 41.5[/tex]

And for the Q3 we can select the last 4 values 57, 63, 72, 91 and for Q3 we got:

[tex]Q_3= \frac{63+72}{2}= 67.5[/tex]

And then the interquartile range would be:

[tex]IQR =Q_3 -Q_1 = 67.5-41.5 = 26[/tex]

Similar Solved Works

3 answers

1) The crow in this story represents the universal archetype of

1) The crow in this story represents the universal archetype of...
4 answers

Choose the element of heritage that is preserved by each excerpt from the folktale. 'The whole family came and bowed down before

Choose the element of heritage that is preserved by each excerpt from the folktale. "The whole family came and bowed down before the warrior, calling him their preserver and the bravest warrior in all Japan." "Another feast was prepared, more sumptuous than the first. All kinds of fish, prepared in ...
3 answers

The Industrial Revolution, a period of significant change in agriculture and manufacturing, marked a big shift in human society. This change

The Industrial Revolution, a period of significant change in agriculture and manufacturing, marked a big shift in human society. This change had a dramatic effect on economic and social structures. In this task, you will analyze some of the changes brought about by industrialization in Great Britain...
4 answers

What is the measure of ∠EFG in the triangle shown?Question 7 options:A) 57°B) 59°C) 58°D) 56°

What is the measure of ∠EFG in the triangle shown? Question 7 options: A) 57° B) 59° C) 58° D) 56°...
3 answers

Used to map mid ocean ridge

Used to map mid ocean ridge...
10 answers

What was China's position in the cold war?​

What was China's position in the cold war?​...
11 answers

What's ya'll favorite shoes

What's ya'll favorite shoes...
3 answers

Two events, X and Y, are independent of each other. P(Y)= and P(X and Y)=. What is P(X) written as a

Two events, X and Y, are independent of each other. P(Y)= and P(X and Y)=. What is P(X) written as a decimal? Round to the nearest tenth, if necessary. 0.2 0.3 0.4 0.5...
9 answers

Helpmathmathmath math :)

Help math math math math :) [tex]Help math math math math :)[/tex]...
8 answers

What is the cell potential of an electrochemical cell that has the half-reactions shown below? ni2+

What is the cell potential of an electrochemical cell that has the half-reactions shown below? ni2+ + 2e → ni al → a13+ + 3e click for a reduction potential chart o o o o a. -1.93 v b. -1.43 v c. 1.43 v d. 2.61 v...
3 answers

What adjective can i add to this sentence? i feel amazed that my family could meet us this summer.

What adjective can i add to this sentence? i feel amazed that my family could meet us this summer....
3 answers

BocODA metal has a specific heat capacity of 360J/(kg°C).An object made of this metal has a mass of 2.0kg.What is the thermal capacity

B oc OD A metal has a specific heat capacity of 360J/(kg°C). An object made of this metal has a mass of 2.0kg. What is the thermal capacity (heat capacity) of the object?...
10 answers

The square below represent one whole express the shaded area as a fraction a decimal

The square below represent one whole express the shaded area as a fraction a decimal...
4 answers

Why do people in the country fear , the spread of communism ?

Why do people in the country fear , the spread of communism ?...
3 answers

How to form a polynomial with given zeros and degree and multiplicity calculator

How to form a polynomial with given zeros and degree and multiplicity calculator...
4 answers

Why did many native americans claim that the wagon caravans that traveled out west had a repulsive odor

Why did many native americans claim that the wagon caravans that traveled out west had a repulsive odor about them...
3 answers

Which is one Genre of Literature? A. store B. mug C. short story​

Which is one Genre of Literature? A. store B. mug C. short story​...
4 answers

What the answers to these>

What the answers to these> [tex]What the answers to these>[/tex]...
3 answers

Loans can come with different repayment options. Which option will always be most logical?

Loans can come with different repayment options. Which option will always be most logical?...
8 answers

Asap 25 points and brainliest (financial math)What is a downside of receiving a tax refund?

Asap 25 points and brainliest (financial math) What is a downside of receiving a tax refund?...

-- 0.019942--