Berikut data tinggi bibit pohon (cm) di kampus Poltesa : $81, 79, 82, 83, 80, 78, 80, 87, 82, 82$ Hitunglah: $1$ . simpangan baku $2$ . varian $3$ . derajat bebas $4$ . koefisien keragaman $5$ . Kuartil $3$ $6$ . desil $6$ $7$ . Persentil $45$

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Grade 7

Divide decimals

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Q. Berikut data tinggi bibit pohon (cm) di kampus Poltesa :

81, 79, 82, 83, 80, 78, 80, 87, 82, 82

Hitunglah:

1

. simpangan baku

2

. varian

3

. derajat bebas

4

. koefisien keragaman

5

. Kuartil

3

6

. desil

6

7

. Persentil

45

Calculate Mean: First, let's find the mean of the data. $\newline$ Mean = $(81 + 79 + 82 + 83 + 80 + 78 + 80 + 87 + 82 + 82) / 10$ $\newline$ Mean = $814 / 10$ $\newline$ Mean = $81.4$
Deviation and Sum: Next, we calculate each value's deviation from the mean, square those deviations, and sum them up. $\newline$ Sum of squared deviations = $(81 - 81.4)^2 + (79 - 81.4)^2 + (82 - 81.4)^2 + (83 - 81.4)^2 + (80 - 81.4)^2 + (78 - 81.4)^2 + (80 - 81.4)^2 + (87 - 81.4)^2 + (82 - 81.4)^2 + (82 - 81.4)^2$ $\newline$ Sum of squared deviations = $(-0.4)^2 + (-2.4)^2 + (0.6)^2 + (1.6)^2 + (-1.4)^2 + (-3.4)^2 + (-1.4)^2 + (5.6)^2 + (0.6)^2 + (0.6)^2$ $\newline$ Sum of squared deviations = $0.16 + 5.76 + 0.36 + 2.56 + 1.96 + 11.56 + 1.96 + 31.36 + 0.36 + 0.36$ $\newline$ Sum of squared deviations = $$55$.$44$
Calculate Variance: Now, we find the variance by dividing the sum of squared deviations by the degrees of freedom.$\newline$Degrees of freedom = $n - 1$$\newline$Degrees of freedom = $10 - 1$$\newline$Degrees of freedom = $9$$\newline$Variance = Sum of squared deviations / Degrees of freedom$\newline$Variance = $55.44 / 9$$\newline$Variance = $6.16$
Find Standard Deviation: To get the standard deviation, we take the square root of the variance.$\newline$Standard deviation = $\sqrt{\text{Variance}}$$\newline$Standard deviation = $\sqrt{6.16}$$\newline$Standard deviation = $2.48$
Coefficient of Variation: The coefficient of variation is calculated by dividing the standard deviation by the mean and multiplying by $100$ to get a percentage.$\newline$Coefficient of variation = $(\text{Standard deviation} / \text{Mean}) \times 100$$\newline$Coefficient of variation = $(2.48 / 81.4) \times 100$$\newline$Coefficient of variation = $3.05\%$
Calculate Q$3$: For the third quartile ($Q_3$), we need to find the value below which $75\%$ of the data lies. Since we have $10$ data points, the position of $Q_3$ is the $7.5$th value.$\newline$We'll need to arrange the data in ascending order and then find the value at the $7.5$th position.$\newline$Ordered data: $78$, $79$, $80$, $80$, $75\%$$0$, $75\%$$1$, $75\%$$1$, $75\%$$1$, $75\%$$4$, $75\%$$5$$\newline$$Q_3$ is between the $75\%$$7$th and $75\%$$8$th value, so we average them.$\newline$$75\%$$9$$\newline$$10$$0$
Find $D_6$: The sixth decile ($D_6$) is the value below which $60\%$ of the data lies. The position of $D_6$ is the $6$th value in the ordered data.$\newline$$D_6 = 82$
Calculate $P_{45}$: For the $45$th percentile ($P_{45}$), we find the value below which $45\%$ of the data lies. The position of $P_{45}$ is the $4.5$th value.$\newline$$P_{45}$ is between the $4$th and $5$th value, so we average them.$\newline$$P_{45} = \frac{80 + 81}{2}$$\newline$$P_{45} = 80.5$