Solved on Feb 21, 2024

Determine how the median changes when 15 is added to a data set of 5 numbers: [13, 24, 18, 12, 29]. The median can stay the same, decrease by 1.5, or increase by 1.5.

STEP 1

Assumptions
1. We have an initial data set: $13, 24, 18, 12, 29$ .
2. We want to determine the effect on the median when adding the number $15$ to the data set.
3. The median is the middle value of an ordered data set.

STEP 2

First, we need to order the initial data set from smallest to largest to find the median.
$Data\, set: 12, 13, 18, 24, 29$

STEP 3

Since there are 5 numbers in the data set, the median is the third number when the data is ordered.
$Median = 18$

STEP 4

Now, we add the number $15$ to the data set and order it again.
$New\, data\, set: 12, 13, 15, 18, 24, 29$

STEP 5

With the new data set having 6 numbers, the median will be the average of the third and fourth numbers.
$Median = \frac{15 + 18}{2}$

STEP 6

Calculate the new median.
$Median = \frac{15 + 18}{2} = \frac{33}{2} = 16.5$

STEP 7

Compare the initial median with the new median to determine the change.
$Change\, in\, median = New\, median - Initial\, median$

STEP 8

Calculate the change in median.
$Change\, in\, median = 16.5 - 18 = -1.5$

STEP 9

Since the change in median is negative, the median decreases by $1.5$ when we add $15$ to the data set.
The correct answer is: Decrease, 1.5.

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Determine how the median changes when 15 is added to a data set of 5 numbers: [13, 24, 18, 12, 29]. The median can stay the same, decrease by 1.5, or increase by 1.5.

STEP 1

Assumptions
1. We have an initial data set: $13, 24, 18, 12, 29$ .
2. We want to determine the effect on the median when adding the number $15$ to the data set.
3. The median is the middle value of an ordered data set.

STEP 2

First, we need to order the initial data set from smallest to largest to find the median.
$Data\, set: 12, 13, 18, 24, 29$

STEP 3

Since there are 5 numbers in the data set, the median is the third number when the data is ordered.
$Median = 18$

STEP 4

Now, we add the number $15$ to the data set and order it again.
$New\, data\, set: 12, 13, 15, 18, 24, 29$

STEP 5

With the new data set having 6 numbers, the median will be the average of the third and fourth numbers.
$Median = \frac{15 + 18}{2}$

STEP 6

Calculate the new median.
$Median = \frac{15 + 18}{2} = \frac{33}{2} = 16.5$

STEP 7

Compare the initial median with the new median to determine the change.
$Change\, in\, median = New\, median - Initial\, median$

STEP 8

Calculate the change in median.
$Change\, in\, median = 16.5 - 18 = -1.5$

STEP 9

Since the change in median is negative, the median decreases by $1.5$ when we add $15$ to the data set.
The correct answer is: Decrease, 1.5.

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Determine how the median changes when 15 is added to a data set of 5 numbers: [13, 24, 18, 12, 29]. The median can stay the same, decrease by 1.5, or increase by 1.5.

STEP 1

Assumptions1. We have an initial data set: 13,24,18,12,2913, 24, 18, 12, 2913,24,18,12,29.2. We want to determine the effect on the median when adding the number 151515 to the data set.3. The median is the middle value of an ordered data set.

STEP 2

First, we need to order the initial data set from smallest to largest to find the median.Data set:12,13,18,24,29Data\, set: 12, 13, 18, 24, 29Dataset:12,13,18,24,29

STEP 3

Since there are 5 numbers in the data set, the median is the third number when the data is ordered.Median=18Median = 18Median=18

STEP 4

Now, we add the number 151515 to the data set and order it again.New data set:12,13,15,18,24,29New\, data\, set: 12, 13, 15, 18, 24, 29Newdataset:12,13,15,18,24,29

STEP 5

With the new data set having 6 numbers, the median will be the average of the third and fourth numbers.Median=15+182Median = \frac{15 + 18}{2}Median=215+18​

STEP 6

Calculate the new median.Median=15+182=332=16.5Median = \frac{15 + 18}{2} = \frac{33}{2} = 16.5Median=215+18​=233​=16.5

STEP 7

Compare the initial median with the new median to determine the change.Change in median=New median−Initial medianChange\, in\, median = New\, median - Initial\, medianChangeinmedian=Newmedian−Initialmedian

STEP 8

Calculate the change in median.Change in median=16.5−18=−1.5Change\, in\, median = 16.5 - 18 = -1.5Changeinmedian=16.5−18=−1.5

STEP 9

Since the change in median is negative, the median decreases by 1.51.51.5 when we add 151515 to the data set.The correct answer is: Decrease, 1.5.

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Assumptions
1. We have an initial data set: $13, 24, 18, 12, 29$ .
2. We want to determine the effect on the median when adding the number $15$ to the data set.
3. The median is the middle value of an ordered data set.

First, we need to order the initial data set from smallest to largest to find the median.
$Data\, set: 12, 13, 18, 24, 29$

Since there are 5 numbers in the data set, the median is the third number when the data is ordered.
$Median = 18$

Now, we add the number $15$ to the data set and order it again.
$New\, data\, set: 12, 13, 15, 18, 24, 29$

With the new data set having 6 numbers, the median will be the average of the third and fourth numbers.
$Median = \frac{15 + 18}{2}$

Calculate the new median.
$Median = \frac{15 + 18}{2} = \frac{33}{2} = 16.5$

Compare the initial median with the new median to determine the change.
$Change\, in\, median = New\, median - Initial\, median$

Calculate the change in median.
$Change\, in\, median = 16.5 - 18 = -1.5$

Since the change in median is negative, the median decreases by $1.5$ when we add $15$ to the data set.
The correct answer is: Decrease, 1.5.