Task 1

You can find the solution to this problem in the Descriptive Statistics – tasks 1-2.xlsx file:

• Sheet: Task 1

Interpreting the Results

• Paid-plan Students

• • Mean: Among students who watched between 1 and 100 minutes in 2021, the average minutes watched by paid-plan students increased significantly from Q4 2021 to Q4 2022, from approximately 33.80 minutes to about 273.02 minutes. This suggests a substantial increase in engagement among this group of initially low-engagement-paid-plan students.
  • Median: The median minutes these low-engagement-paid-plan students watched increased from Q4 2021 to Q4 2022, from 26.33 minutes to 40.28 minutes. While this increase is not as dramatic as the increase in the mean, it indicates that the typical student in this group (i.e., the student in the middle of the distribution) also increased their engagement. This suggests that the increase in engagement was more widespread among paid-plan students and not solely driven by a few outliers.
  • Standard Deviation: The standard deviation for these low-engagement-paid-plan students increased substantially from 28.21 minutes in Q4 2021 to 854.58 minutes in Q4 2022. This indicates a much larger variability in the minutes watched by these students in Q4 2022 compared to Q4 2021. This could be due to a broader range of engagement levels among the students in Q4 2022, with some students watching very little content and others watching a lot of content.

These results suggest that paid-plan students who were initially low-engagement in 2021 significantly increased their engagement in 2022. But the increased standard deviation indicates a broader range of engagement levels among these students in 2022. Understanding the reasons behind this variability could provide valuable insights for further boosting engagement. For instance, the factors that motivated the students who significantly increased their engagement might be leveraged to encourage increased engagement among other students.

• Free-Plan Students

• • Mean: Among students who watched between 1 and 100 minutes in 2021, the average minutes watched by free-plan students increased from about 25.39 minutes in Q4 2021 to about 117.64 minutes in Q4 2022. This suggests that overall engagement among these initially low-engagement-free-plan students increased during this period. But the extent of this increase is less than what was observed for similar low-engagement-paid-plan students, suggesting that while these free-plan students are watching more content, they’re still not as engaged as the equivalent group of paid-plan students.
  • Median: Interestingly, the median minutes watched by these low-engagement-free-plan students decreased from Q4 2021 to Q4 2022, from 14.17 minutes to 11.83 minutes. This indicates that engagement decreased for the typical student in this group (i.e., the student in the middle of the distribution). The increase in the mean might be driven by a small number of free-plan students who significantly increased their engagement in Q4 2022, while the majority did not increase their engagement or even reduced it.
  • Standard Deviation: The standard deviation for the low-engagement-free-plan students increased from 26.23 minutes in Q4 2021 to 468.93 minutes in Q4 2022. This indicates a more significant variability in the minutes watched by these students in Q4 2022 compared to Q4 2021. The behavior of these students then became more diverse in Q4 2022, with some watching a lot of content and others watching very little.

These results suggest a complex picture for the initially low-engagement-free-plan students. While the mean minutes watched increased—signifying an increase in overall engagement—the median minutes watched decreased, indicating that the typical student in this group did not increase their engagement. This discrepancy and the increased standard deviation suggest that a small number of students within this group might significantly increase their engagement while the majority did not. This might imply the need for targeted strategies to boost engagement among the broader population of initially low-engagement-free-plan students.

• Paid vs Free-Plan Students

On average, low-engagement-paid students initially increased their watching time more significantly than the free-plan students from Q4 2021 to Q4 2022. This could suggest that paid-plan students find more value in the platform, possibly due to premium features or content that are available to them.In contrast, the median watch time decreased for free-plan students, suggesting that the typical free-plan student in this group did not increase their engagement. This discrepancy might indicate that the strategies or features designed to increase engagement are more effective for paid-plan students. It could also suggest that the monetary investment leads to increased usage due to a desire to get their money’s worth.

Based on the findings, the platform is more successful in increasing engagement among students who make a monetary investment (i.e., paid-plan students). But the increased variability, especially among paid-plan students, indicates that there are likely differences in how individual students are responding to the platform’s offerings. Therefore, personalized approaches might be beneficial in boosting engagement, and further analysis could help understand the factors that drive increased engagement among paid- and free-plan students.

Task 2

You can find the solution to this problem in the Descriptive Statistics – tasks 1-2.xlsx file:

• Sheet: Task 2

Skewness is a fundamental measure of probability distribution asymmetry in a dataset. It reveals whether the observations are concentrated more on one side of the distribution. This metric helps us understand how the data deviates from a normal distribution and provides insights into its underlying structure. A positive skewness value (higher than 0) indicates a right-skewed distribution, while a negative skewness value (lower than 0) points to a left-skewed distribution. A symmetrical distribution has a skewness value of 0, indicating a balanced data spread around the mean.

For paid-plan students, the skewness increased from 0.63 in Q4 2021 to 7.07 in Q4 2022.

The skewness for free-plan students increased from 1.17 in Q4 2021 to 15.06 in Q4 2022, indicating positive skewness.

Positive skew (right-skew) occurs when the data is not symmetrical around the mean, forming a long tail on its right side. This signifies that most of the distribution’s observations are concentrated to the left of the peak. Positive skewness can have several implications.

The mean is larger than the median in a right-skewed distribution because the distribution tail pulls the mean to the right. This observation is confirmed by the mean and median values in the two years. An increasing skewness suggests that more students watch significantly more content than most over time, pulling the mean upwards.

In both cases, the mean is higher than the median (33.80 > 26.33 in 2021 and 273.02 > 40.28 in 2022).

As a result, the mean is no longer a good central tendency indicator, and it cannot accurately reflect the typical value of the dataset. Note that skewness tells us the direction of outliers but doesn’t indicate the number that occurs.

Kurtosis measures the degree of tailedness—the weight of the tails relative to the rest of the distribution. In other words, it shows how much of the data is in the tails compared to the center. Located farthest from the center, the tails represent the regions where data points are more dispersed—suggesting the presence of more extreme values. If a distribution is heavy-tailed—i.e., more data in the tails—it exhibits high kurtosis. Meanwhile, a low kurtosis occurs when the data is more evenly distributed between the tails and the center or the distribution is light-tailed.

For paid-plan students, the kurtosis increased from -0.85 in Q4 2021 to 58.48 in Q4 2022.

The kurtosis increased from free-plan students—from 0.36 in Q4 2021 to 315.76 in Q4 2022. 

Kurtosis values greater than 0 indicate that the data has heavier tails and a sharper peak than the normal distribution (leptokurtic). A leptokurtic distribution has a high positive kurtosis, suggesting that it’s very peaked and has a relatively large number of outliers. This type has a higher frequency of extreme values or outliers. The increase in kurtosis over time suggests more extreme cases in the data in Q4 2022 than in Q4 2021, particularly for free-plan students.

Overall, the increasing skewness and kurtosis for both groups from Q4 2021 to Q4 2022 suggest a growing number of students watching significantly more content than the majority. This is especially true for free-plan students with a higher skewness and kurtosis in Q4 2022 than paid-plan students.