- Consider the following data on the categories of YouTube Shorts and their views. The table shows the number of YouTube Shorts in each category that have been classified as either “High Views” (more than 1,000,000 views) or “Low Views” (1,000,000 views or less).
| Category | High Views | Low Views | Total |
|---|---|---|---|
| Music | 50 | 100 | 150 |
| Comedy | 30 | 170 | 200 |
| Education | 20 | 180 | 200 |
| Gaming | 40 | 160 | 200 |
| Travel | 10 | 190 | 200 |
| Total | 150 | 800 | 950 |
What is the probability that a randomly selected YouTube Short is in the Music Category?
What is the probability that a randomly selected YouTube Short has High Views?
What is the probability that a randomly selected YouTube Short has Low Views?
If a YouTube Short is known to be in the Comedy category, what is the probability that it has High Views?
If a YouTube Short is known to have High Views, what is the probability that it is in the Gaming category?
Solution discussion:
i. Probability that a randomly selected YouTube Short is in the Music category
To find this probability, we use the formula: P(Music)=Total Music Shorts / Total Shorts
Total Music Shorts = 150
Total Shorts = 950
P(Music)=150/ 950 = 0.1579
ii. Probability that a randomly selected YouTube Short has High Views
To find this probability, we use the formula: P(High Views)=Total High Views Shorts / Total Shorts
Total High Views Shorts = 150
Total Shorts = 950
P(High Views)=150/ 950 = 0.1579
iii. Probability that a randomly selected YouTube Short has Low Views
To find this probability, we use the formula: P(Low Views)=Total Low Views Shorts / Total Shorts
Total Low Views Shorts = 800
Total Shorts = 950
P(Low Views)=800 / 950 = 0.8421
iv. Probability that a YouTube Short in the Comedy category has High Views
To find this conditional probability, we use the formula: P(High Views | Comedy)=High Views Comedy Shorts / Total Comedy Shorts
High Views Comedy Shorts = 30
Total Comedy Shorts = 200
P(High Views | Comedy)= 30/ 200= 0.15
v. Probability that a YouTube Short with High Views is in the Gaming category
To find this conditional probability, we use the formula: P(Gaming | High Views)=High Views Gaming Shorts/ Total High Views Shorts
High Views Gaming Shorts = 40
Total High Views Shorts = 150
P(Gaming | High Views)=40/ 150= 0.2667
Summary
- Probability that a randomly selected YouTube Short is in the Music category: 0.1579
- Probability that a randomly selected YouTube Short has High Views: 0.1579
- Probability that a randomly selected YouTube Short has Low Views: 0.8421
- Probability that a YouTube Short in the Comedy category has High Views: 0.15
- Probability that a YouTube Short with High Views is in the Gaming category: 0.2667
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2. Use 4 month moving average, and 5 month moving average too. For which moving average Mean Square Error is less.
Solution Discussion:
4-Month Moving Average
The 4-month moving average is calculated by taking the average of the views for the past 4 months.
| Month | Views | 4-Month Moving Average |
|---|---|---|
| May-23 | 16141 | (10484 + 10884 + 13372 + 14742) / 4 = 12370.5 |
| Jun-23 | 17210 | (10884 + 13372 + 14742 + 16141) / 4 = 13784.75 |
| Jul-23 | 17303 | (13372 + 14742 + 16141 + 17210) / 4 = 15366.25 |
| Aug-23 | 18132 | (14742 + 16141 + 17210 + 17303) / 4 = 16349 |
| Sep-23 | 18208 | (16141 + 17210 + 17303 + 18132) / 4 = 17196.5 |
| Oct-23 | 19099 | (17210 + 17303 + 18132 + 18208) / 4 = 17713.25 |
| Nov-23 | 20936 | (17303 + 18132 + 18208 + 19099) / 4 = 18185.5 |
| Dec-23 | 21914 | (18132 + 18208 + 19099 + 20936) / 4 = 19093.75 |
| Jan-24 | 22892 | (18208 + 19099 + 20936 + 21914) / 4 = 20039.25 |
| Feb-24 | 23870 | (19099 + 20936 + 21914 + 22892) / 4 = 21210.25 |
| Mar-24 | 24848 | (20936 + 21914 + 22892 + 23870) / 4 = 22403 |
| Apr-24 | 25826 | (21914 + 22892 + 23870 + 24848) / 4 = 23381 |
| May-24 | 26803 | (22892 + 23870 + 24848 + 25826) / 4 = 24359 |
| Jun-24 | 27781 | (23870 + 24848 + 25826 + 26803) / 4 = 25336.75 |
5-Month Moving Average
The 5-month moving average is calculated by taking the average of the views for the past 5 months.
| Month | Views | 5-Month Moving Average |
|---|---|---|
| Jun-23 | 17210 | (10484 + 10884 + 13372 + 14742 + 16141) / 5 = 13124.6 |
| Jul-23 | 17303 | (10884 + 13372 + 14742 + 16141 + 17210) / 5 = 14469.8 |
| Aug-23 | 18132 | (13372 + 14742 + 16141 + 17210 + 17303) / 5 = 15753.6 |
| Sep-23 | 18208 | (14742 + 16141 + 17210 + 17303 + 18132) / 5 = 16705.6 |
| Oct-23 | 19099 | (16141 + 17210 + 17303 + 18132 + 18208) / 5 = 17398.8 |
| Nov-23 | 20936 | (17210 + 17303 + 18132 + 18208 + 19099) / 5 = 17990.4 |
| Dec-23 | 21914 | (17303 + 18132 + 18208 + 19099 + 20936) / 5 = 18735.6 |
| Jan-24 | 22892 | (18132 + 18208 + 19099 + 20936 + 21914) / 5 = 19657.8 |
| Feb-24 | 23870 | (18208 + 19099 + 20936 + 21914 + 22892) / 5 = 20609.8 |
| Mar-24 | 24848 | (19099 + 20936 + 21914 + 22892 + 23870) / 5 = 21742.2 |
| Apr-24 | 25826 | (20936 + 21914 + 22892 + 23870 + 24848) / 5 = 22892 |
| May-24 | 26803 | (21914 + 22892 + 23870 + 24848 + 25826) / 5 = 23870 |
| Jun-24 | 27781 | (22892 + 23870 + 24848 + 25826 + 26803) / 5 = 24848 |
Mean Square Error (MSE) Calculation
4-Month Moving Average
Given the data and the 4-Month Moving Average calculations:
| Month | Actual Views | 4-Month Moving Average |
|---|---|---|
| May-23 | 16141 | 12370.5 |
| Jun-23 | 17210 | 13784.75 |
| Jul-23 | 17303 | 15366.25 |
| Aug-23 | 18132 | 16349 |
| Sep-23 | 18208 | 17196.5 |
| Oct-23 | 19099 | 17713.25 |
| Nov-23 | 20936 | 18185.5 |
| Dec-23 | 21914 | 19093.75 |
| Jan-24 | 22892 | 20039.25 |
| Feb-24 | 23870 | 21210.25 |
| Mar-24 | 24848 | 22403 |
| Apr-24 | 25826 | 23381 |
| May-24 | 26803 | 24359 |
| Jun-24 | 27781 | 25336.75 |
Step-by-Step Calculation for 4-Month Moving Average MSE
| Month | Actual Views | 4-Month Moving Average | Error |
|---|---|---|---|
| May-23 | 16141 | 12370.5 | 3770.5 |
| Jun-23 | 17210 | 13784.75 | 3425.25 |
| Jul-23 | 17303 | 15366.25 | 1936.75 |
| Aug-23 | 18132 | 16349 | 1783 |
| Sep-23 | 18208 | 17196.5 | 1011.5 |
| Oct-23 | 19099 | 17713.25 | 1385.75 |
| Nov-23 | 20936 | 18185.5 | 2749.5 |
| Dec-23 | 21914 | 19093.75 | 2820.25 |
| Jan-24 | 22892 | 20039.25 | 2852.75 |
| Feb-24 | 23870 | 21210.25 | 2659.75 |
| Mar-24 | 24848 | 22403 | 2445 |
| Apr-24 | 25826 | 23381 | 2445 |
| May-24 | 26803 | 24359 | 1444 |
| Jun-24 | 27781 | 25336.75 | 2444.25 |
| Month | Squared Error |
|---|---|
| May-23 | 14218040.25 |
| Jun-23 | 11732756.56 |
| Jul-23 | 3740735.56 |
| Aug-23 | 3181489 |
| Sep-23 | 1023152.25 |
| Oct-23 | 1920740.56 |
| Nov-23 | 7567110.25 |
| Dec-23 | 7958055.06 |
| Jan-24 | 8138171.56 |
| Feb-24 | 7074080.56 |
| Mar-24 | 5979025 |
| Apr-24 | 5717425 |
| May-24 | 2085136 |
| Jun-24 | 5977360.56 |
5-Month Moving Average
Given the data and the 5-Month Moving Average calculations:
| Month | Actual Views | 5-Month Moving Average |
|---|---|---|
| Jun-23 | 17210 | 13124.6 |
| Jul-23 | 17303 | 14469.8 |
| Aug-23 | 18132 | 15753.6 |
| Sep-23 | 18208 | 16705.6 |
| Oct-23 | 19099 | 17398.8 |
| Nov-23 | 20936 | 17990.4 |
| Dec-23 | 21914 | 18735.6 |
| Jan-24 | 22892 | 19657.8 |
| Feb-24 | 23870 | 20609.8 |
| Mar-24 | 24848 | 21742.2 |
| Apr-24 | 25826 | 22892 |
| May-24 | 26803 | 23870 |
| Jun-24 | 27781 | 24848 |
Step-by-Step Calculation for 5-Month Moving Average MSE
| Month | Actual Views | 5-Month Moving Average | Error |
|---|---|---|---|
| Jun-23 | 17210 | 13124.6 | 4085.4 |
| Jul-23 | 17303 | 14469.8 | 2833.2 |
| Aug-23 | 18132 | 15753.6 | 2378.4 |
| Sep-23 | 18208 | 16705.6 | 1502.4 |
| Oct-23 | 19099 | 17398.8 | 1699.2 |
| Nov-23 | 20936 | 17990.4 | 2945.6 |
| Dec-23 | 21914 | 18735.6 | 318.4 |
| Jan-24 | 22892 | 19657.8 | 3234.2 |
| Feb-24 | 23870 | 20609.8 | 3260.2 |
| Mar-24 | 24848 | 21742.2 | 3105.8 |
| Apr-24 | 25826 | 22892 | 2934 |
| May-24 | 26803 | 23870 | 1933 |
| Jun-24 | 27781 | 24848 | 1933 |
| Month | Squared Error |
|---|---|
| Jun-23 | 16691118.76 |
| Jul-23 | 8027624.64 |
| Aug-23 | 5656065.76 |
| Sep-23 | 2257209.76 |
| Oct-23 | 2886720.64 |
| Nov-23 | 8679960.96 |
| Dec-23 | 101378.56 |
| Jan-24 | 10459723.24 |
| Feb-24 | 10638504.04 |
| Mar-24 | 9635556.64 |
| Apr-24 | 8605956 |
| May-24 | 3734689 |
| Jun-24 | 3734689 |
Conclusion
- MSE for 4-Month Moving Average: 6305633.48
- MSE for 5-Month Moving Average: 5699534.17
Therefore, the Mean Square Error (MSE) is lower for the 5-Month Moving Average compared to the 4-Month Moving Average, indicating that the 5-Month Moving Average provides a better fit to the data.
- a) Use an appropriate chart to show the contribution of each category of sales with conclusion. Rahul has this channel and offers a variety of content to users.
| Category | Average Views |
|---|---|
| Music | 1,200,000 |
| Comedy | 800,000 |
| Education | 600,000 |
| Gaming | 900,000 |
| Travel | 700,000 |
Solution discussion:
Let’s calculate the total views and the percentage contribution for each category:
Total Views = 1,200,000 + 800,000 + 600,000 + 900,000 + 700,000 = 4,200,000
Now, calculate the percentage contribution for each category:
- Music: 1,200,000/ 4,200,000×100%=28.57%
- Comedy: 800,000 / 4,200,000×100%=19.05%
- Education: 600,000/ 4,200,000×100%=14.29%
- Gaming: 900,0004,200,000×100%=21.43%
- Travel: 700,0004,200,000×100%=16.67%
A pie chart is suitable for visualizing the contribution of each category based on average views. Here’s how the pie chart would represent the data:
- Music: 28.57%
- Comedy: 19.05%
- Education: 14.29%
- Gaming: 21.43%
- Travel: 16.67%
Each category is represented as a slice of the pie chart, with the size of each slice proportional to the percentage it contributes to the total average views.
Pie charts are effective for showing the distribution of parts of a whole and are particularly useful when you want to emphasize the proportionality of each category relative to the others.
- b) Suppose we have the duration (in seconds) of 10 YouTube Shorts videos: 120, 130, 140, 125, 135, 150, 128, 132, 142, and 155. Calculate the mean (average) duration of these videos.
Solution discussion:
To calculate the mean (average) duration of the 10 YouTube Shorts videos, we add up all the durations and divide by the number of videos:
Durations of videos: 120, 130, 140, 125, 135, 150, 128, 132, 142, 155
Step-by-step calculation:
- Add all the durations together:120+130+140+125+135+150+128+132+142+155=1357
- Divide by the number of videos (which is 10):Mean (average) duration=1357/ 10=135.7
Therefore, the mean duration of these YouTube Shorts videos is 135.7 seconds.
Note: These post is meant for students educational purpose only.
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