For 37 students with three assessment columns (Tugas, UAS and a second Tugas), compute the mean, median, mode, range, sample variance, standard deviation and quartiles of each column.

Step-by-step solution

1. 1

   Total each column and divide by n = 37. Summing carefully:

   $\sum \text{Tugas} = 2606, \qquad \sum \text{UAS} = 2579, \qquad \sum \text{TUGAS} = 2906$

   $\bar{x}_{\text{Tugas}} = \frac{2606}{37} = 70.4324, \quad \bar{x}_{\text{UAS}} = \frac{2579}{37} = 69.7027, \quad \bar{x}_{\text{TUGAS}} = \frac{2906}{37} = 78.5405$

   The totals are worth re-adding: a single mis-keyed row shifts a mean by up to $2.4$ points here.

2. 2

   Find the medians. With $n = 37$ (odd) the median is the $19$th value of the sorted list, with no averaging needed:

   $\text{Median}_{\text{Tugas}} = 76, \qquad \text{Median}_{\text{UAS}} = 77, \qquad \text{Median}_{\text{TUGAS}} = 82$

   Every median exceeds its mean, the signature of a left-skewed distribution — caused here by the two students scoring $0$.

3. 3

   Identify the modes. Counting frequencies: Tugas is bimodal at $83$ and $85$ (three times each); UAS is bimodal at $81$ and $86$ (four times each); TUGAS has a single mode at $81$ (four times). Modes this weak — a top frequency of only three or four out of $37$ — carry little information about a nearly continuous score variable.

4. 4

   Compute the sample variance and standard deviation. Using $s^2 = \dfrac{\sum(x_i - \bar x)^2}{n-1}$ with $n - 1 = 36$:

   $s^2_{\text{Tugas}} = 427.3634,\ s_{\text{Tugas}} = 20.6728$

   $s^2_{\text{UAS}} = 406.9925,\ s_{\text{UAS}} = 20.1741$

   $s^2_{\text{TUGAS}} = 190.3664,\ s_{\text{TUGAS}} = 13.7973$

5. 5

   Report ranges and quartiles. Minimum, maximum and the Tukey quartiles $Q_1, Q_2, Q_3$:

   Column	Min	Max	Range	$Q_1$	$Q_2$	$Q_3$	IQR
   Tugas	0	90	90	61	76	85	24
   UAS	0	92	92	60	77	81	21
   TUGAS	32	94	62	74	82	86	12

6. 6

   Interpret the spread, and flag the outliers. The two rows of $(0, 0, 32)$ are almost certainly absentees rather than genuine performance. By the $1.5\times$IQR rule the Tugas fence is $61 - 1.5(24) = 25$, so both zeros are outliers; the UAS fence is $60 - 1.5(21) = 28.5$, likewise; and the TUGAS fence is $74 - 1.5(12) = 56$, so both $32$s are outliers there too. Excluding those two students would raise the Tugas mean to $\tfrac{2606}{35} = 74.46$ and cut its standard deviation sharply. The third column is genuinely the most homogeneous ($s = 13.80$ versus $\approx 20$ for the other two), and it stays so even after the outliers are removed.