Solved on Jan 12, 2024

Calculate the range of the data set with $n=10$ observations: $\text{range} = \max(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9) - \min(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9)$ .

STEP 1

Assumptions
1. The sample size is $n=10$ .
2. The data set consists of the following numbers: $63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9$ .
3. The range of a data set is the difference between the largest and smallest data values.

STEP 2

To find the range, we need to identify the largest and smallest numbers in the data set.

STEP 3

Scan through the data set to find the smallest number.
$\text{Smallest number} = \min(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9) = 46.1$

STEP 4

Scan through the data set to find the largest number.
$\text{Largest number} = \max(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9) = 81.9$

STEP 5

Now that we have the smallest and largest numbers, we can calculate the range by subtracting the smallest number from the largest number.
$\text{Range} = \text{Largest number} - \text{Smallest number}$

STEP 6

Substitute the identified smallest and largest numbers into the range formula.
$\text{Range} = 81.9 - 46.1$

STEP 7

Calculate the range.
$\text{Range} = 81.9 - 46.1 = 35.8$
The range of this data set is $35.8$ .

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Calculate the range of the data set with $n=10$ observations: $\text{range} = \max(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9) - \min(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9)$ .

STEP 1

Assumptions
1. The sample size is $n=10$ .
2. The data set consists of the following numbers: $63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9$ .
3. The range of a data set is the difference between the largest and smallest data values.

STEP 2

To find the range, we need to identify the largest and smallest numbers in the data set.

STEP 3

Scan through the data set to find the smallest number.
$\text{Smallest number} = \min(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9) = 46.1$

STEP 4

Scan through the data set to find the largest number.
$\text{Largest number} = \max(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9) = 81.9$

STEP 5

Now that we have the smallest and largest numbers, we can calculate the range by subtracting the smallest number from the largest number.
$\text{Range} = \text{Largest number} - \text{Smallest number}$

STEP 6

Substitute the identified smallest and largest numbers into the range formula.
$\text{Range} = 81.9 - 46.1$

STEP 7

Calculate the range.
$\text{Range} = 81.9 - 46.1 = 35.8$
The range of this data set is $35.8$ .

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STEP 1

STEP 2

To find the range, we need to identify the largest and smallest numbers in the data set.

STEP 3

STEP 4

Scan through the data set to find the largest number.Largest number=max⁡(63.6,81.9,74.5,66.8,53.5,57.4,69.6,46.1,81.9,81.9)=81.9\text{Largest number} = \max(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9) = 81.9Largest number=max(63.6,81.9,74.5,66.8,53.5,57.4,69.6,46.1,81.9,81.9)=81.9

STEP 5

Now that we have the smallest and largest numbers, we can calculate the range by subtracting the smallest number from the largest number.Range=Largest number−Smallest number\text{Range} = \text{Largest number} - \text{Smallest number}Range=Largest number−Smallest number

STEP 6

Substitute the identified smallest and largest numbers into the range formula.Range=81.9−46.1\text{Range} = 81.9 - 46.1Range=81.9−46.1

STEP 7

Calculate the range.Range=81.9−46.1=35.8\text{Range} = 81.9 - 46.1 = 35.8Range=81.9−46.1=35.8The range of this data set is 35.835.835.8.

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Scan through the data set to find the largest number.
$\text{Largest number} = \max(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9) = 81.9$

Now that we have the smallest and largest numbers, we can calculate the range by subtracting the smallest number from the largest number.
$\text{Range} = \text{Largest number} - \text{Smallest number}$

Substitute the identified smallest and largest numbers into the range formula.
$\text{Range} = 81.9 - 46.1$

Calculate the range.
$\text{Range} = 81.9 - 46.1 = 35.8$
The range of this data set is $35.8$ .