Solved on Feb 01, 2024

List the sample in ascending order, use comma to separate. Find the range, number of classes, and class width. Complete the frequency distribution by listing the lower and upper class limits for each class and its frequency, including the maximum value(s) to the last class if the limits don't include it/them.

STEP 1

Assumptions
1. We have a list of numbers that we need to analyze.
2. We need to determine the range of the sample.
3. We need to find out how many classes there are.
4. We need to calculate the class width.
5. We need to create a frequency distribution.

STEP 2

The sample is already listed in ascending order, so there is no need to reorder it.

STEP 3

To find the range, we subtract the smallest number in the sample from the largest number.
$Range = Largest\, number - Smallest\, number$

STEP 4

Identify the smallest and largest numbers in the sample.
Smallest number: $5$ Largest number: $34$

STEP 5

Calculate the range using the identified smallest and largest numbers.
$Range = 34 - 5$

STEP 6

Compute the range.
$Range = 29$
The range is $29$ .

STEP 7

To determine how many classes there are, we look at the options provided: $5$ or $0^{6}$ . Since $0^{6}$ is not a meaningful number of classes, we choose $5$ .
The number of classes is $5$ .

STEP 8

To calculate the class width, we divide the range by the number of classes.
$Class\, width = \frac{Range}{Number\, of\, classes}$

STEP 9

Plug in the values for the range and the number of classes to calculate the class width.
$Class\, width = \frac{29}{5}$

STEP 10

Compute the class width.
$Class\, width = 5.8$
Since class width should be a whole number and we should round up to ensure all data points are included, the class width is $6$ .
The class width is $6$ .

STEP 11

To complete the frequency distribution, we need to list the lower and upper class limits for each class and its frequency.

STEP 12

Determine the lower limit of the first class. It will be the smallest number in the sample, which is $5$ .

STEP 13

Determine the upper limit of the first class by adding the class width to the lower limit of the first class.
$Upper\, limit\, of\, first\, class = Lower\, limit\, of\, first\, class + Class\, width - 1$

STEP 14

Compute the upper limit of the first class.
$Upper\, limit\, of\, first\, class = 5 + 6 - 1 = 10$

STEP 15

Continue determining the lower and upper limits for the subsequent classes by adding the class width to the previous upper limit and subtracting $1$ for the upper limit of each class.

STEP 16

List the lower and upper class limits for each class and count the frequency of numbers within those limits.
Class 1: $5-10$ (Frequency: $4$ ) Class 2: $11-16$ (Frequency: $6$ ) Class 3: $17-22$ (Frequency: $2$ ) Class 4: $23-28$ (Frequency: $7$ ) Class 5: $29-34$ (Frequency: $9$ )
Note: Include the maximum value(s) to the last class if the limits don't include it/them. Since the last class includes the maximum value of $34$ , there is no need to adjust the limits.

STEP 17

The completed frequency distribution is as follows:
\begin{tabular}{|c|c|} \hline Class & Frequency \\ \hline 5-10 & 4 \\ 11-16 & 6 \\ 17-22 & 2 \\ 23-28 & 7 \\ 29-34 & 9 \\ \hline \end{tabular}

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STEP 1

Assumptions
1. We have a list of numbers that we need to analyze.
2. We need to determine the range of the sample.
3. We need to find out how many classes there are.
4. We need to calculate the class width.
5. We need to create a frequency distribution.

STEP 2

The sample is already listed in ascending order, so there is no need to reorder it.

STEP 3

To find the range, we subtract the smallest number in the sample from the largest number.
$Range = Largest\, number - Smallest\, number$

STEP 4

Identify the smallest and largest numbers in the sample.
Smallest number: $5$ Largest number: $34$

STEP 5

Calculate the range using the identified smallest and largest numbers.
$Range = 34 - 5$

STEP 6

Compute the range.
$Range = 29$
The range is $29$ .

STEP 7

To determine how many classes there are, we look at the options provided: $5$ or $0^{6}$ . Since $0^{6}$ is not a meaningful number of classes, we choose $5$ .
The number of classes is $5$ .

STEP 8

To calculate the class width, we divide the range by the number of classes.
$Class\, width = \frac{Range}{Number\, of\, classes}$

STEP 9

Plug in the values for the range and the number of classes to calculate the class width.
$Class\, width = \frac{29}{5}$

STEP 10

Compute the class width.
$Class\, width = 5.8$
Since class width should be a whole number and we should round up to ensure all data points are included, the class width is $6$ .
The class width is $6$ .

STEP 11

To complete the frequency distribution, we need to list the lower and upper class limits for each class and its frequency.

STEP 12

Determine the lower limit of the first class. It will be the smallest number in the sample, which is $5$ .

STEP 13

Determine the upper limit of the first class by adding the class width to the lower limit of the first class.
$Upper\, limit\, of\, first\, class = Lower\, limit\, of\, first\, class + Class\, width - 1$

STEP 14

Compute the upper limit of the first class.
$Upper\, limit\, of\, first\, class = 5 + 6 - 1 = 10$

STEP 15

Continue determining the lower and upper limits for the subsequent classes by adding the class width to the previous upper limit and subtracting $1$ for the upper limit of each class.

STEP 16

STEP 17

The completed frequency distribution is as follows:
\begin{tabular}{|c|c|} \hline Class & Frequency \\ \hline 5-10 & 4 \\ 11-16 & 6 \\ 17-22 & 2 \\ 23-28 & 7 \\ 29-34 & 9 \\ \hline \end{tabular}

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STEP 1

Assumptions1. We have a list of numbers that we need to analyze.2. We need to determine the range of the sample.3. We need to find out how many classes there are.4. We need to calculate the class width.5. We need to create a frequency distribution.

STEP 2

The sample is already listed in ascending order, so there is no need to reorder it.

STEP 3

To find the range, we subtract the smallest number in the sample from the largest number.Range=Largest number−Smallest numberRange = Largest\, number - Smallest\, numberRange=Largestnumber−Smallestnumber

STEP 4

Identify the smallest and largest numbers in the sample.Smallest number: 555 Largest number: 343434

STEP 5

Calculate the range using the identified smallest and largest numbers.Range=34−5Range = 34 - 5Range=34−5

STEP 6

Compute the range.Range=29Range = 29Range=29The range is 292929.

STEP 7

To determine how many classes there are, we look at the options provided: 555 or 060^{6}06. Since 060^{6}06 is not a meaningful number of classes, we choose 555.The number of classes is 555.

STEP 8

To calculate the class width, we divide the range by the number of classes.Class width=RangeNumber of classesClass\, width = \frac{Range}{Number\, of\, classes}Classwidth=NumberofclassesRange​

STEP 9

Plug in the values for the range and the number of classes to calculate the class width.Class width=295Class\, width = \frac{29}{5}Classwidth=529​

STEP 10

Compute the class width.Class width=5.8Class\, width = 5.8Classwidth=5.8Since class width should be a whole number and we should round up to ensure all data points are included, the class width is 666.The class width is 666.

STEP 11

To complete the frequency distribution, we need to list the lower and upper class limits for each class and its frequency.

STEP 12

Determine the lower limit of the first class. It will be the smallest number in the sample, which is 555.

STEP 13

STEP 14

Compute the upper limit of the first class.Upper limit of first class=5+6−1=10Upper\, limit\, of\, first\, class = 5 + 6 - 1 = 10Upperlimitoffirstclass=5+6−1=10

STEP 15

Continue determining the lower and upper limits for the subsequent classes by adding the class width to the previous upper limit and subtracting 111 for the upper limit of each class.

STEP 16

STEP 17

The completed frequency distribution is as follows:\begin{tabular}{|c|c|} \hline Class & Frequency \\ \hline 5-10 & 4 \\ 11-16 & 6 \\ 17-22 & 2 \\ 23-28 & 7 \\ 29-34 & 9 \\ \hline \end{tabular}

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Assumptions
1. We have a list of numbers that we need to analyze.
2. We need to determine the range of the sample.
3. We need to find out how many classes there are.
4. We need to calculate the class width.
5. We need to create a frequency distribution.

To find the range, we subtract the smallest number in the sample from the largest number.
$Range = Largest\, number - Smallest\, number$

Identify the smallest and largest numbers in the sample.
Smallest number: $5$ Largest number: $34$

Calculate the range using the identified smallest and largest numbers.
$Range = 34 - 5$

Compute the range.
$Range = 29$
The range is $29$ .

To determine how many classes there are, we look at the options provided: $5$ or $0^{6}$ . Since $0^{6}$ is not a meaningful number of classes, we choose $5$ .
The number of classes is $5$ .

To calculate the class width, we divide the range by the number of classes.
$Class\, width = \frac{Range}{Number\, of\, classes}$

Plug in the values for the range and the number of classes to calculate the class width.
$Class\, width = \frac{29}{5}$

Compute the class width.
$Class\, width = 5.8$
Since class width should be a whole number and we should round up to ensure all data points are included, the class width is $6$ .
The class width is $6$ .

Determine the lower limit of the first class. It will be the smallest number in the sample, which is $5$ .

Compute the upper limit of the first class.
$Upper\, limit\, of\, first\, class = 5 + 6 - 1 = 10$

Continue determining the lower and upper limits for the subsequent classes by adding the class width to the previous upper limit and subtracting $1$ for the upper limit of each class.

The completed frequency distribution is as follows:
\begin{tabular}{|c|c|} \hline Class & Frequency \\ \hline 5-10 & 4 \\ 11-16 & 6 \\ 17-22 & 2 \\ 23-28 & 7 \\ 29-34 & 9 \\ \hline \end{tabular}