QuestionFind the interquartile range of the data set: $10, 3, 7, 6, 9, 12, 13$ .

Studdy Solution

STEP 1

Assumptions1. The given data set is $10,3,7,6,9,12,13$ . The interquartile range (QR) is defined as the difference between the third quartile (Q3) and the first quartile (Q1).

STEP 2

First, we need to arrange the data set in ascending order.

STEP 3

Arrange the given data set in ascending order.
$3,6,7,9,10,12,13$

STEP 4

Next, we need to find the first quartile (Q1). This is the median of the first half of the data set. If the number of data points is odd, do not include the middle number.

STEP 5

Find the first quartile (Q1) of the data set.
$Q1 = Median\, of\, (3,,7)$

STEP 6

Calculate the first quartile (Q1).
$Q1 =6$

STEP 7

Next, we need to find the third quartile (Q3). This is the median of the second half of the data set. If the number of data points is odd, do not include the middle number.

STEP 8

Find the third quartile (Q3) of the data set.
$Q3 = Median\, of\, (10,12,13)$

STEP 9

Calculate the third quartile (Q3).
$Q3 =12$

STEP 10

Now that we have the first and third quartiles, we can find the interquartile range (QR) by subtracting the first quartile from the third quartile.
$QR = Q3 - Q$

STEP 11

Plug in the values for Q3 and Q to calculate the interquartile range.
$QR = -6$

STEP 12

Calculate the interquartile range.
$QR =12 -6 =6$ The interquartile range for the data set is6.

Was this helpful?

QuestionFind the interquartile range of the data set: $10, 3, 7, 6, 9, 12, 13$ .

Studdy Solution

STEP 1

Assumptions1. The given data set is $10,3,7,6,9,12,13$ . The interquartile range (QR) is defined as the difference between the third quartile (Q3) and the first quartile (Q1).

STEP 2

First, we need to arrange the data set in ascending order.

STEP 3

Arrange the given data set in ascending order.
$3,6,7,9,10,12,13$

STEP 4

Next, we need to find the first quartile (Q1). This is the median of the first half of the data set. If the number of data points is odd, do not include the middle number.

STEP 5

Find the first quartile (Q1) of the data set.
$Q1 = Median\, of\, (3,,7)$

STEP 6

Calculate the first quartile (Q1).
$Q1 =6$

STEP 7

Next, we need to find the third quartile (Q3). This is the median of the second half of the data set. If the number of data points is odd, do not include the middle number.

STEP 8

Find the third quartile (Q3) of the data set.
$Q3 = Median\, of\, (10,12,13)$

STEP 9

Calculate the third quartile (Q3).
$Q3 =12$

STEP 10

Now that we have the first and third quartiles, we can find the interquartile range (QR) by subtracting the first quartile from the third quartile.
$QR = Q3 - Q$

STEP 11

Plug in the values for Q3 and Q to calculate the interquartile range.
$QR = -6$

STEP 12

Calculate the interquartile range.
$QR =12 -6 =6$ The interquartile range for the data set is6.

Get Studdy

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.

QuestionFind the interquartile range of the data set: 10,3,7,6,9,12,1310, 3, 7, 6, 9, 12, 1310,3,7,6,9,12,13.

Studdy Solution

STEP 1

Assumptions1. The given data set is 10,3,7,6,9,12,1310,3,7,6,9,12,1310,3,7,6,9,12,13 . The interquartile range (QR) is defined as the difference between the third quartile (Q3) and the first quartile (Q1).

STEP 2

First, we need to arrange the data set in ascending order.

STEP 3

Arrange the given data set in ascending order.3,6,7,9,10,12,133,6,7,9,10,12,133,6,7,9,10,12,13

STEP 4

Next, we need to find the first quartile (Q1). This is the median of the first half of the data set. If the number of data points is odd, do not include the middle number.

STEP 5

Find the first quartile (Q1) of the data set.Q1=Median of (3,,7)Q1 = Median\, of\, (3,,7)Q1=Medianof(3,,7)

STEP 6

Calculate the first quartile (Q1).Q1=6Q1 =6Q1=6

STEP 7

Next, we need to find the third quartile (Q3). This is the median of the second half of the data set. If the number of data points is odd, do not include the middle number.

STEP 8

Find the third quartile (Q3) of the data set.Q3=Median of (10,12,13)Q3 = Median\, of\, (10,12,13)Q3=Medianof(10,12,13)

STEP 9

Calculate the third quartile (Q3).Q3=12Q3 =12Q3=12

STEP 10

Now that we have the first and third quartiles, we can find the interquartile range (QR) by subtracting the first quartile from the third quartile.QR=Q3−QQR = Q3 - QQR=Q3−Q

STEP 11

Plug in the values for Q3 and Q to calculate the interquartile range.QR=−6QR = -6QR=−6

STEP 12

Calculate the interquartile range.QR=12−6=6QR =12 -6 =6QR=12−6=6The interquartile range for the data set is6.

Get Studdy

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.

QuestionFind the interquartile range of the data set: $10, 3, 7, 6, 9, 12, 13$ .

Assumptions1. The given data set is $10,3,7,6,9,12,13$ . The interquartile range (QR) is defined as the difference between the third quartile (Q3) and the first quartile (Q1).

Arrange the given data set in ascending order.
$3,6,7,9,10,12,13$

Find the first quartile (Q1) of the data set.
$Q1 = Median\, of\, (3,,7)$

Calculate the first quartile (Q1).
$Q1 =6$

Find the third quartile (Q3) of the data set.
$Q3 = Median\, of\, (10,12,13)$

Calculate the third quartile (Q3).
$Q3 =12$

Now that we have the first and third quartiles, we can find the interquartile range (QR) by subtracting the first quartile from the third quartile.
$QR = Q3 - Q$

Plug in the values for Q3 and Q to calculate the interquartile range.
$QR = -6$

Calculate the interquartile range.
$QR =12 -6 =6$ The interquartile range for the data set is6.