Math / Data & Statistics

QuestionConsider the below data for ALL PARTS of this question: $78 \quad 83926885$
What is the INNER QUARTILE RANGE? $\qquad$ Note: Enter X.X AT LEAST ONE DIGIT BEFORE THE DECIMAL, ONE AFTER and round up AFTER all calculations. Thus, 7 is entered as 7.0; -3.562 is entered as -3.6 ; 0.3750 is entered as $0.4 ; 17.351$ is entered as 17.4 $\square$ A

Studdy Solution

STEP 1

What is this asking? Find the difference between the 75th percentile and the 25th percentile of this small dataset. Watch out! Don't forget to sort the data before finding the quartiles!
Also, remember to round up at the very end, not during intermediate steps.

STEP 2

1. Sort the data
2. Find the 25th percentile (Q1)
3. Find the 75th percentile (Q3)
4. Calculate the Interquartile Range (IQR)

STEP 3

Alright, let's wrangle these numbers into order from least to greatest!
We've got $68, 78, 83, 85, 92$ .
Much better!
This makes it way easier to see where the quartiles are.

STEP 4

Since we have 5 data points, the position of the 25th percentile (Q1) is $(5 + 1) \cdot \frac{25}{100} = 6 \cdot 0.25 = 1.5$ .
This means Q1 is between the 1st and 2nd values.

STEP 5

To find Q1, we'll take the average of the 1st and 2nd values: $\frac{68 + 78}{2} = \frac{146}{2} = 73$ .
So, our Q1 is 73!

STEP 6

Similarly, the position of the 75th percentile (Q3) is $(5 + 1) \cdot \frac{75}{100} = 6 \cdot 0.75 = 4.5$ .
This puts Q3 right between the 4th and 5th values.

STEP 7

Let's average those values to find Q3: $\frac{85 + 92}{2} = \frac{177}{2} = 88.5$ .
So, Q3 is 88.5!

STEP 8

The Interquartile Range (IQR) is simply the difference between Q3 and Q1.
So, $IQR = Q3 - Q1 = 88.5 - 73 = 15.5$ .

STEP 9

Since the problem asked us to round up after all calculations, and our result has exactly one digit after the decimal, we don't need to change anything!
Our final IQR is 15.5!

STEP 10

The Interquartile Range is 15.5.

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Studdy Solution

STEP 1

What is this asking? Find the difference between the 75th percentile and the 25th percentile of this small dataset. Watch out! Don't forget to sort the data before finding the quartiles!
Also, remember to round up at the very end, not during intermediate steps.

STEP 2

1. Sort the data
2. Find the 25th percentile (Q1)
3. Find the 75th percentile (Q3)
4. Calculate the Interquartile Range (IQR)

STEP 3

Alright, let's wrangle these numbers into order from least to greatest!
We've got $68, 78, 83, 85, 92$ .
Much better!
This makes it way easier to see where the quartiles are.

STEP 4

Since we have 5 data points, the position of the 25th percentile (Q1) is $(5 + 1) \cdot \frac{25}{100} = 6 \cdot 0.25 = 1.5$ .
This means Q1 is between the 1st and 2nd values.

STEP 5

To find Q1, we'll take the average of the 1st and 2nd values: $\frac{68 + 78}{2} = \frac{146}{2} = 73$ .
So, our Q1 is 73!

STEP 6

Similarly, the position of the 75th percentile (Q3) is $(5 + 1) \cdot \frac{75}{100} = 6 \cdot 0.75 = 4.5$ .
This puts Q3 right between the 4th and 5th values.

STEP 7

Let's average those values to find Q3: $\frac{85 + 92}{2} = \frac{177}{2} = 88.5$ .
So, Q3 is 88.5!

STEP 8

The Interquartile Range (IQR) is simply the difference between Q3 and Q1.
So, $IQR = Q3 - Q1 = 88.5 - 73 = 15.5$ .

STEP 9

Since the problem asked us to round up after all calculations, and our result has exactly one digit after the decimal, we don't need to change anything!
Our final IQR is 15.5!

STEP 10

The Interquartile Range is 15.5.

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Studdy Solution

STEP 1

What is this asking? Find the difference between the **75th percentile** and the **25th percentile** of this small dataset. Watch out! Don't forget to **sort the data** before finding the quartiles!Also, remember to round up at the very end, not during intermediate steps.

STEP 2

1. Sort the data2. Find the 25th percentile (Q1)3. Find the 75th percentile (Q3)4. Calculate the Interquartile Range (IQR)

STEP 3

Alright, let's **wrangle these numbers** into order from least to greatest!We've got 68,78,83,85,9268, 78, 83, 85, 9268,78,83,85,92.Much better!This makes it way easier to see where the quartiles are.

STEP 4

Since we have **5 data points**, the position of the **25th percentile (Q1)** is (5+1)⋅25100=6⋅0.25=1.5(5 + 1) \cdot \frac{25}{100} = 6 \cdot 0.25 = 1.5(5+1)⋅10025​=6⋅0.25=1.5.This means Q1 is between the **1st and 2nd values**.

STEP 5

To find Q1, we'll take the average of the 1st and 2nd values: 68+782=1462=73\frac{68 + 78}{2} = \frac{146}{2} = 73268+78​=2146​=73.So, our **Q1 is 73**!

STEP 6

Similarly, the position of the **75th percentile (Q3)** is (5+1)⋅75100=6⋅0.75=4.5(5 + 1) \cdot \frac{75}{100} = 6 \cdot 0.75 = 4.5(5+1)⋅10075​=6⋅0.75=4.5.This puts Q3 right between the **4th and 5th values**.

STEP 7

Let's average those values to find Q3: 85+922=1772=88.5\frac{85 + 92}{2} = \frac{177}{2} = 88.5285+92​=2177​=88.5.So, **Q3 is 88.5**!

STEP 8

The **Interquartile Range (IQR)** is simply the difference between Q3 and Q1.So, IQR=Q3−Q1=88.5−73=15.5IQR = Q3 - Q1 = 88.5 - 73 = 15.5IQR=Q3−Q1=88.5−73=15.5.

STEP 9

Since the problem asked us to round up after all calculations, and our result has exactly one digit after the decimal, we don't need to change anything!Our **final IQR is 15.5**!

STEP 10

The **Interquartile Range** is **15.5**.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Find the difference between the 75th percentile and the 25th percentile of this small dataset. Watch out! Don't forget to sort the data before finding the quartiles!
Also, remember to round up at the very end, not during intermediate steps.

1. Sort the data
2. Find the 25th percentile (Q1)
3. Find the 75th percentile (Q3)
4. Calculate the Interquartile Range (IQR)

Alright, let's wrangle these numbers into order from least to greatest!
We've got $68, 78, 83, 85, 92$ .
Much better!
This makes it way easier to see where the quartiles are.

Since we have 5 data points, the position of the 25th percentile (Q1) is $(5 + 1) \cdot \frac{25}{100} = 6 \cdot 0.25 = 1.5$ .
This means Q1 is between the 1st and 2nd values.

To find Q1, we'll take the average of the 1st and 2nd values: $\frac{68 + 78}{2} = \frac{146}{2} = 73$ .
So, our Q1 is 73!

Similarly, the position of the 75th percentile (Q3) is $(5 + 1) \cdot \frac{75}{100} = 6 \cdot 0.75 = 4.5$ .
This puts Q3 right between the 4th and 5th values.

Let's average those values to find Q3: $\frac{85 + 92}{2} = \frac{177}{2} = 88.5$ .
So, Q3 is 88.5!

The Interquartile Range (IQR) is simply the difference between Q3 and Q1.
So, $IQR = Q3 - Q1 = 88.5 - 73 = 15.5$ .

Since the problem asked us to round up after all calculations, and our result has exactly one digit after the decimal, we don't need to change anything!
Our final IQR is 15.5!

The Interquartile Range is 15.5.