QuestionDetermine the best measure of center (mean, median, mode) for the data set $\{5,7,4,1,2,1,1\}$ .

Studdy Solution

STEP 1

Assumptions1. The data set is $\{5,7,4,1,,1,1\}$ . We need to calculate the mean, median, and mode of the data set3. We will then determine which measure of center most accurately summarizes the data

STEP 2

First, let's calculate the mean of the data set. The mean is the sum of all values divided by the number of values.
$Mean = \frac{Sum\, of\, all\, values}{Number\, of\, values}$

STEP 3

Now, plug in the given values to calculate the mean.
$Mean = \frac{5+7++1+2+1+1}{7}$

STEP 4

Calculate the mean.
$Mean = \frac{21}{7} =3$

STEP 5

Next, let's calculate the median of the data set. The median is the middle value when the data is arranged in ascending order. If there is an even number of values, the median is the average of the two middle values.
First, arrange the data in ascending order.
$\{1,1,1,2,4,5,7\}$

STEP 6

The median is the fourth value in the ordered list, which is2.
$Median =2$

STEP 7

Finally, let's calculate the mode of the data set. The mode is the value that appears most frequently in the data set.
From the data set, we can see that the number1 appears three times, which is more than any other number.
$Mode =1$

STEP 8

Now that we have the mean, median, and mode, we can determine which measure of center most accurately summarizes the data.
In this case, the mode is the most accurate measure of center because it represents the most frequent value in the data set. The mean and median are both higher than the mode, which could be due to the influence of the higher values in the data set.Therefore, the mode most accurately summarizes the data set.

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QuestionDetermine the best measure of center (mean, median, mode) for the data set $\{5,7,4,1,2,1,1\}$ .

Studdy Solution

STEP 1

Assumptions1. The data set is $\{5,7,4,1,,1,1\}$ . We need to calculate the mean, median, and mode of the data set3. We will then determine which measure of center most accurately summarizes the data

STEP 2

First, let's calculate the mean of the data set. The mean is the sum of all values divided by the number of values.
$Mean = \frac{Sum\, of\, all\, values}{Number\, of\, values}$

STEP 3

Now, plug in the given values to calculate the mean.
$Mean = \frac{5+7++1+2+1+1}{7}$

STEP 4

Calculate the mean.
$Mean = \frac{21}{7} =3$

STEP 5

Next, let's calculate the median of the data set. The median is the middle value when the data is arranged in ascending order. If there is an even number of values, the median is the average of the two middle values.
First, arrange the data in ascending order.
$\{1,1,1,2,4,5,7\}$

STEP 6

The median is the fourth value in the ordered list, which is2.
$Median =2$

STEP 7

Finally, let's calculate the mode of the data set. The mode is the value that appears most frequently in the data set.
From the data set, we can see that the number1 appears three times, which is more than any other number.
$Mode =1$

STEP 8

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QuestionDetermine the best measure of center (mean, median, mode) for the data set {5,7,4,1,2,1,1}\{5,7,4,1,2,1,1\}{5,7,4,1,2,1,1}.

Studdy Solution

STEP 1

Assumptions1. The data set is {5,7,4,1,,1,1}\{5,7,4,1,,1,1\}{5,7,4,1,,1,1} . We need to calculate the mean, median, and mode of the data set3. We will then determine which measure of center most accurately summarizes the data

STEP 2

First, let's calculate the mean of the data set. The mean is the sum of all values divided by the number of values.Mean=Sum of all valuesNumber of valuesMean = \frac{Sum\, of\, all\, values}{Number\, of\, values}Mean=NumberofvaluesSumofallvalues​

STEP 3

Now, plug in the given values to calculate the mean.Mean=5+7++1+2+1+17Mean = \frac{5+7++1+2+1+1}{7}Mean=75+7++1+2+1+1​

STEP 4

Calculate the mean.Mean=217=3Mean = \frac{21}{7} =3Mean=721​=3

STEP 5

STEP 6

The median is the fourth value in the ordered list, which is2.Median=2Median =2Median=2

STEP 7

Finally, let's calculate the mode of the data set. The mode is the value that appears most frequently in the data set.From the data set, we can see that the number1 appears three times, which is more than any other number.Mode=1Mode =1Mode=1

STEP 8

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QuestionDetermine the best measure of center (mean, median, mode) for the data set $\{5,7,4,1,2,1,1\}$ .

Assumptions1. The data set is $\{5,7,4,1,,1,1\}$ . We need to calculate the mean, median, and mode of the data set3. We will then determine which measure of center most accurately summarizes the data

First, let's calculate the mean of the data set. The mean is the sum of all values divided by the number of values.
$Mean = \frac{Sum\, of\, all\, values}{Number\, of\, values}$

Now, plug in the given values to calculate the mean.
$Mean = \frac{5+7++1+2+1+1}{7}$

Calculate the mean.
$Mean = \frac{21}{7} =3$

The median is the fourth value in the ordered list, which is2.
$Median =2$

Finally, let's calculate the mode of the data set. The mode is the value that appears most frequently in the data set.
From the data set, we can see that the number1 appears three times, which is more than any other number.
$Mode =1$