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Dari kumpulan data 50 responden, dihasilkan tabel distribusi frekuensi dibawah, tentukan nilai Desil ke -7 dari data tersebut ...

Nilai
Frekuensi

73-77
3

78-82
6

83-87
20

88-92
12

93-97
9

$20$ . Dari kumpulan data $50$ responden, dihasilkan tabel distribusi frekuensi dibawah, tentukan nilai Desil ke $-7$ dari data tersebut ... $\newline$ \begin{tabular}{|c|c|} $\newline$ \hline Nilai & Frekuensi \\ $\newline$ \hline $73-77$ & $3$ \\ $\newline$ $78-82$ & $6$ \\ $\newline$ $83-87$ & $20$ \\ $\newline$ $88-92$ & $12$ \\ $\newline$ $93-97$ & $9$ \\ $\newline$ \hline $\newline$ \end{tabular}

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Multiply and divide rational expressions

Full solution

Q.

20

. Dari kumpulan data

50

responden, dihasilkan tabel distribusi frekuensi dibawah, tentukan nilai Desil ke

-7

dari data tersebut ...

\newline

\begin{tabular}{|c|c|}

\newline

\hline Nilai & Frekuensi \\

\newline

\hline

73-77

&

3

\\

\newline

78-82

&

6

\\

\newline

83-87

&

20

\\

\newline

88-92

&

12

\\

\newline

93-97

&

9

\\

\newline

\hline

\newline

\end{tabular}

Calculate Total Data Points: To find the $7^{\text{th}}$ decile, we need to determine the position in the data set. The formula for the position of the $k^{\text{th}}$ decile is $P = \frac{k(N + 1)}{10}$ , where $N$ is the total number of data points.
Find Position of $7$ th Decile: First, let's calculate the total number of data points, $N$ . We add up the frequencies: $3 + 6 + 20 + 12 + 9 = 50$ .
Identify Class Interval: Now, we find the position of the $7$ th decile using the formula $P = \frac{7(50 + 1)}{10} = \frac{7(51)}{10} = \frac{357}{10} = 35.7$ . We round up to the nearest whole number, so $P = 36$ .
Calculate Decile Value: Next, we need to find which class interval the $36$ th position falls into. We add the cumulative frequencies until we reach or pass the $36$ th position: $3$ ( $73$ - $77$ ), $3 + 6 = 9$ ( $78$ - $82$ ), $9 + 20 = 29$ ( $83$ - $36$ $0$ ), $36$ $1$ ( $36$ $2$ - $36$ $3$ ). The $36$ th position is in the $36$ $2$ - $36$ $3$ interval.
Calculate Decile Value: Next, we need to find which class interval the $36$ th position falls into. We add the cumulative frequencies until we reach or pass the $36$ th position: $3$ ( $73$ - $77$ ), $3 + 6 = 9$ ( $78$ - $82$ ), $9 + 20 = 29$ ( $83$ - $36$ $0$ ), $36$ $1$ ( $36$ $2$ - $36$ $3$ ). The $36$ th position is in the $36$ $2$ - $36$ $3$ interval.To find the $36$ $7$ th decile value, we use the formula: $36$ $8$ , where $36$ $9$ is the lower limit of the class containing the decile, $3$ $0$ is the total number of data points, $3$ $1$ is the decile number, $3$ $2$ is the cumulative frequency before the decile class, $3$ $3$ is the frequency of the decile class, and $3$ $4$ is the class width.
Calculate Decile Value: Next, we need to find which class interval the $36$ th position falls into. We add the cumulative frequencies until we reach or pass the $36$ th position: $3$ ( $73$ - $77$ ), $3 + 6 = 9$ ( $78$ - $82$ ), $9 + 20 = 29$ ( $83$ - $36$ $0$ ), $36$ $1$ ( $36$ $2$ - $36$ $3$ ). The $36$ th position is in the $36$ $2$ - $36$ $3$ interval.To find the $36$ $7$ th decile value, we use the formula: $36$ $8$ , where $36$ $9$ is the lower limit of the class containing the decile, $3$ $0$ is the total number of data points, $3$ $1$ is the decile number, $3$ $2$ is the cumulative frequency before the decile class, $3$ $3$ is the frequency of the decile class, and $3$ $4$ is the class width.The lower limit $36$ $9$ for the $36$ $2$ - $36$ $3$ interval is $36$ $2$ . The cumulative frequency before the $36$ $2$ - $36$ $3$ interval is $73$ $1$ . The frequency $3$ $3$ for the $36$ $2$ - $36$ $3$ interval is $73$ $5$ . The class width $3$ $4$ is $73$ $7$ .
Calculate Decile Value: Next, we need to find which class interval the $36^{\text{th}}$ position falls into. We add the cumulative frequencies until we reach or pass the $36^{\text{th}}$ position: $3$ ( $73-77$ ), $3 + 6 = 9$ ( $78-82$ ), $9 + 20 = 29$ ( $83-87$ ), $29 + 12 = 41$ ( $88-92$ ). The $36^{\text{th}}$ position is in the $88-92$ interval.To find the $36^{\text{th}}$ $2$ decile value, we use the formula: $36^{\text{th}}$ $3$ , where $36^{\text{th}}$ $4$ is the lower limit of the class containing the decile, $36^{\text{th}}$ $5$ is the total number of data points, $36^{\text{th}}$ $6$ is the decile number, $36^{\text{th}}$ $7$ is the cumulative frequency before the decile class, $36^{\text{th}}$ $8$ is the frequency of the decile class, and $36^{\text{th}}$ $9$ is the class width.The lower limit $36^{\text{th}}$ $4$ for the $88-92$ interval is $3$ $2$ . The cumulative frequency before the $88-92$ interval is $3$ $4$ . The frequency $36^{\text{th}}$ $8$ for the $88-92$ interval is $3$ $7$ . The class width $36^{\text{th}}$ $9$ is $3$ $9$ .Now we plug the values into the formula: $73-77$ $0$ .

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