Solved on Sep 24, 2023

Calculate the Interquartile Range (IQR) for the two columns of data: $\{0, 5, 11, 14, 15, 19, 20, 20, 26, 33, 33, 34\}$ and $\{7, 8, 14, 15, 24, 27, 29, 30, 32, 45, 49\}$ .

STEP 1

Assumptions1. We have two columns of values. . We need to find the Interquartile Range (QR) for each column.
3. The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

STEP 2

First, we need to arrange the values in each column in ascending order.
Column10,5,11,15,19,20,20,26,33,33,34,40Column27,8,14,15,16,24,27,29,30,32,45,49

STEP 3

Next, we need to find the first quartile (Q1) and the third quartile (Q3) for each column.Q1 is the median of the first half of the data and Q3 is the median of the second half of the data.

STEP 4

Calculate Q1 for Column1. Since we have an even number of data points, the median is the average of the two middle numbers.
$Q1_{Column1} = \frac{11 +15}{2}$

STEP 5

Calculate Q1 for Column1.
$Q1_{Column1} = \frac{11 +15}{2} =13$

STEP 6

Calculate Q3 for Column1. $Q3_{Column1} = \frac{33 +33}{2}$

STEP 7

Calculate Q3 for Column1.
$Q3_{Column1} = \frac{33 +33}{2} =33$

STEP 8

Calculate Q1 for Column2.
$Q1_{Column2} = \frac{14 +15}{2}$

STEP 9

Calculate Q for Column2.
$Q_{Column2} = \frac{14 +15}{2} =14.5$

STEP 10

Calculate Q3 for Column2.
$Q3_{Column2} = \frac{30 +32}{2}$

STEP 11

Calculate Q3 for Column.
$Q3_{Column} = \frac{30 +32}{} =31$

STEP 12

Now that we have Q and Q for each column, we can calculate the Interquartile Range (QR) for each column. The IQR is calculated as Q - Q.
$QR_{Column} = Q_{Column} - Q_{Column}$ $QR_{Column2} = Q_{Column2} - Q_{Column2}$

STEP 13

Calculate IQR for Column.
$QR_{Column} =33 -13 =20$

STEP 14

Calculate IQR for Column2.
$QR_{Column2} =31 -14. =16.$ The Interquartile Range (QR) for Column is20 and for Column2 is16..

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Calculate the Interquartile Range (IQR) for the two columns of data: $\{0, 5, 11, 14, 15, 19, 20, 20, 26, 33, 33, 34\}$ and $\{7, 8, 14, 15, 24, 27, 29, 30, 32, 45, 49\}$ .

STEP 1

Assumptions1. We have two columns of values. . We need to find the Interquartile Range (QR) for each column.
3. The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

STEP 2

First, we need to arrange the values in each column in ascending order.
Column10,5,11,15,19,20,20,26,33,33,34,40Column27,8,14,15,16,24,27,29,30,32,45,49

STEP 3

Next, we need to find the first quartile (Q1) and the third quartile (Q3) for each column.Q1 is the median of the first half of the data and Q3 is the median of the second half of the data.

STEP 4

Calculate Q1 for Column1. Since we have an even number of data points, the median is the average of the two middle numbers.
$Q1_{Column1} = \frac{11 +15}{2}$

STEP 5

Calculate Q1 for Column1.
$Q1_{Column1} = \frac{11 +15}{2} =13$

STEP 6

Calculate Q3 for Column1. $Q3_{Column1} = \frac{33 +33}{2}$

STEP 7

Calculate Q3 for Column1.
$Q3_{Column1} = \frac{33 +33}{2} =33$

STEP 8

Calculate Q1 for Column2.
$Q1_{Column2} = \frac{14 +15}{2}$

STEP 9

Calculate Q for Column2.
$Q_{Column2} = \frac{14 +15}{2} =14.5$

STEP 10

Calculate Q3 for Column2.
$Q3_{Column2} = \frac{30 +32}{2}$

STEP 11

Calculate Q3 for Column.
$Q3_{Column} = \frac{30 +32}{} =31$

STEP 12

Now that we have Q and Q for each column, we can calculate the Interquartile Range (QR) for each column. The IQR is calculated as Q - Q.
$QR_{Column} = Q_{Column} - Q_{Column}$ $QR_{Column2} = Q_{Column2} - Q_{Column2}$

STEP 13

Calculate IQR for Column.
$QR_{Column} =33 -13 =20$

STEP 14

Calculate IQR for Column2.
$QR_{Column2} =31 -14. =16.$ The Interquartile Range (QR) for Column is20 and for Column2 is16..

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STEP 1

Assumptions1. We have two columns of values. . We need to find the Interquartile Range (QR) for each column.3. The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

STEP 2

First, we need to arrange the values in each column in ascending order.Column10,5,11,15,19,20,20,26,33,33,34,40Column27,8,14,15,16,24,27,29,30,32,45,49

STEP 3

Next, we need to find the first quartile (Q1) and the third quartile (Q3) for each column.Q1 is the median of the first half of the data and Q3 is the median of the second half of the data.

STEP 4

Calculate Q1 for Column1. Since we have an even number of data points, the median is the average of the two middle numbers.Q1Column1=11+152Q1_{Column1} = \frac{11 +15}{2}Q1Column1​=211+15​

STEP 5

Calculate Q1 for Column1.Q1Column1=11+152=13Q1_{Column1} = \frac{11 +15}{2} =13Q1Column1​=211+15​=13

STEP 6

Calculate Q3 for Column1.Q3Column1=33+332Q3_{Column1} = \frac{33 +33}{2}Q3Column1​=233+33​

STEP 7

Calculate Q3 for Column1.Q3Column1=33+332=33Q3_{Column1} = \frac{33 +33}{2} =33Q3Column1​=233+33​=33

STEP 8

Calculate Q1 for Column2.Q1Column2=14+152Q1_{Column2} = \frac{14 +15}{2}Q1Column2​=214+15​

STEP 9

Calculate Q for Column2.QColumn2=14+152=14.5Q_{Column2} = \frac{14 +15}{2} =14.5QColumn2​=214+15​=14.5

STEP 10

Calculate Q3 for Column2.Q3Column2=30+322Q3_{Column2} = \frac{30 +32}{2}Q3Column2​=230+32​

STEP 11

Calculate Q3 for Column.Q3Column=30+32=31Q3_{Column} = \frac{30 +32}{} =31Q3Column​=30+32​=31

STEP 12

STEP 13

Calculate IQR for Column.QRColumn=33−13=20QR_{Column} =33 -13 =20QRColumn​=33−13=20

STEP 14

Calculate IQR for Column2.QRColumn2=31−14.=16.QR_{Column2} =31 -14. =16.QRColumn2​=31−14.=16.The Interquartile Range (QR) for Column is20 and for Column2 is16..

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Assumptions1. We have two columns of values. . We need to find the Interquartile Range (QR) for each column.
3. The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

First, we need to arrange the values in each column in ascending order.
Column10,5,11,15,19,20,20,26,33,33,34,40Column27,8,14,15,16,24,27,29,30,32,45,49

Calculate Q1 for Column1. Since we have an even number of data points, the median is the average of the two middle numbers.
$Q1_{Column1} = \frac{11 +15}{2}$

Calculate Q1 for Column1.
$Q1_{Column1} = \frac{11 +15}{2} =13$

Calculate Q3 for Column1. $Q3_{Column1} = \frac{33 +33}{2}$

Calculate Q3 for Column1.
$Q3_{Column1} = \frac{33 +33}{2} =33$

Calculate Q1 for Column2.
$Q1_{Column2} = \frac{14 +15}{2}$

Calculate Q for Column2.
$Q_{Column2} = \frac{14 +15}{2} =14.5$

Calculate Q3 for Column2.
$Q3_{Column2} = \frac{30 +32}{2}$

Calculate Q3 for Column.
$Q3_{Column} = \frac{30 +32}{} =31$

Calculate IQR for Column.
$QR_{Column} =33 -13 =20$

Calculate IQR for Column2.
$QR_{Column2} =31 -14. =16.$ The Interquartile Range (QR) for Column is20 and for Column2 is16..