Solved on Sep 13, 2023

Find the third quartile for the given data: $87, 10, 50, 74, 83, 70, 25, 64, 47, 97, 15, 20, 68, 3, 23$ .

STEP 1

Assumptions1. The given data is quantitative and ungrouped. . The third quartile (Q3) is the value below which75% of the data falls.
3. The data is not yet sorted in ascending order.

STEP 2

First, we need to sort the data in ascending order. This is a necessary step before we can calculate the quartiles.
The sorted data is\begin{tabular}{|r|r|} \hline &10 \\ \hline15 &20 \\ \hline23 &25 \\ \hline47 &50 \\ \hline64 &68 \\ \hline70 &74 \\ \hline83 &87 \\ \hline97 & \\ \hline\end{tabular}

STEP 3

Now, we need to find the position of the third quartile (Q3). The formula to find the position of Q3 is $Q3\, position = \frac{3}{}(n+1)$ where n is the total number of observations.

STEP 4

Calculate the total number of observations (n). In this case, n =14.

STEP 5

Plug in the value of n into the formula to find the position of Q3.
$Q3\, position = \frac{3}{4}(14+1)$

STEP 6

Calculate the position of Q3.
$Q3\, position = \frac{3}{4}(15) =11.25$

STEP 7

Since the position of Q3 is not a whole number, we need to take the average of the11th and12th observations to find Q3.

STEP 8

Identify the11th and12th observations in the sorted data. In this case, the11th observation is74 and the12th observation is83.

STEP 9

Calculate the average of the11th and12th observations to find Q3.
$Q3 = \frac{74 +83}{2}$

STEP 10

Calculate Q3.
$Q3 = \frac{74 +83}{2} =78.5$ The third quartile (Q3) for the given quantitative data is78.5.

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Find the third quartile for the given data: $87, 10, 50, 74, 83, 70, 25, 64, 47, 97, 15, 20, 68, 3, 23$ .

STEP 1

Assumptions1. The given data is quantitative and ungrouped. . The third quartile (Q3) is the value below which75% of the data falls.
3. The data is not yet sorted in ascending order.

STEP 2

First, we need to sort the data in ascending order. This is a necessary step before we can calculate the quartiles.
The sorted data is\begin{tabular}{|r|r|} \hline &10 \\ \hline15 &20 \\ \hline23 &25 \\ \hline47 &50 \\ \hline64 &68 \\ \hline70 &74 \\ \hline83 &87 \\ \hline97 & \\ \hline\end{tabular}

STEP 3

Now, we need to find the position of the third quartile (Q3). The formula to find the position of Q3 is $Q3\, position = \frac{3}{}(n+1)$ where n is the total number of observations.

STEP 4

Calculate the total number of observations (n). In this case, n =14.

STEP 5

Plug in the value of n into the formula to find the position of Q3.
$Q3\, position = \frac{3}{4}(14+1)$

STEP 6

Calculate the position of Q3.
$Q3\, position = \frac{3}{4}(15) =11.25$

STEP 7

Since the position of Q3 is not a whole number, we need to take the average of the11th and12th observations to find Q3.

STEP 8

Identify the11th and12th observations in the sorted data. In this case, the11th observation is74 and the12th observation is83.

STEP 9

Calculate the average of the11th and12th observations to find Q3.
$Q3 = \frac{74 +83}{2}$

STEP 10

Calculate Q3.
$Q3 = \frac{74 +83}{2} =78.5$ The third quartile (Q3) for the given quantitative data is78.5.

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Find the third quartile for the given data: 87,10,50,74,83,70,25,64,47,97,15,20,68,3,2387, 10, 50, 74, 83, 70, 25, 64, 47, 97, 15, 20, 68, 3, 2387,10,50,74,83,70,25,64,47,97,15,20,68,3,23.

STEP 1

Assumptions1. The given data is quantitative and ungrouped. . The third quartile (Q3) is the value below which75% of the data falls.3. The data is not yet sorted in ascending order.

STEP 2

First, we need to sort the data in ascending order. This is a necessary step before we can calculate the quartiles.The sorted data is\begin{tabular}{|r|r|} \hline &10 \\ \hline15 &20 \\ \hline23 &25 \\ \hline47 &50 \\ \hline64 &68 \\ \hline70 &74 \\ \hline83 &87 \\ \hline97 & \\ \hline\end{tabular}

STEP 3

Now, we need to find the position of the third quartile (Q3). The formula to find the position of Q3 isQ3 position=3(n+1)Q3\, position = \frac{3}{}(n+1)Q3position=3​(n+1)where n is the total number of observations.

STEP 4

Calculate the total number of observations (n). In this case, n =14.

STEP 5

Plug in the value of n into the formula to find the position of Q3.Q3 position=34(14+1)Q3\, position = \frac{3}{4}(14+1)Q3position=43​(14+1)

STEP 6

Calculate the position of Q3.Q3 position=34(15)=11.25Q3\, position = \frac{3}{4}(15) =11.25Q3position=43​(15)=11.25

STEP 7

Since the position of Q3 is not a whole number, we need to take the average of the11th and12th observations to find Q3.

STEP 8

Identify the11th and12th observations in the sorted data. In this case, the11th observation is74 and the12th observation is83.

STEP 9

Calculate the average of the11th and12th observations to find Q3.Q3=74+832Q3 = \frac{74 +83}{2}Q3=274+83​

STEP 10

Calculate Q3.Q3=74+832=78.5Q3 = \frac{74 +83}{2} =78.5Q3=274+83​=78.5The third quartile (Q3) for the given quantitative data is78.5.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the third quartile for the given data: $87, 10, 50, 74, 83, 70, 25, 64, 47, 97, 15, 20, 68, 3, 23$ .

Assumptions1. The given data is quantitative and ungrouped. . The third quartile (Q3) is the value below which75% of the data falls.
3. The data is not yet sorted in ascending order.

Now, we need to find the position of the third quartile (Q3). The formula to find the position of Q3 is $Q3\, position = \frac{3}{}(n+1)$ where n is the total number of observations.

Plug in the value of n into the formula to find the position of Q3.
$Q3\, position = \frac{3}{4}(14+1)$

Calculate the position of Q3.
$Q3\, position = \frac{3}{4}(15) =11.25$

Calculate the average of the11th and12th observations to find Q3.
$Q3 = \frac{74 +83}{2}$

Calculate Q3.
$Q3 = \frac{74 +83}{2} =78.5$ The third quartile (Q3) for the given quantitative data is78.5.