question archive The Scenario The amount of time spent daily on communication with friends by people ages '15 to 24 was collected pre-pandemic and post pandemic
The Scenario The amount of time spent daily on communication with friends by people ages '15 to 24 was collected pre-pandemic and post pandemic
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The Scenario The amount of time spent daily on communication with friends by people ages '15 to 24 was collected pre-pandemic and post pandemic. The numerical summaries of the datasets are below. Use the information in the numerical summaries to answer the questions below. Pre-pandemic, May through December 2019. average daily minutes spent communication with friends via texting, phone calls and video chats N Min Q1 Median Q3 Max Mean St. Dev 44,328 3.44 5.22 6.78 9.25 49.29 7.86 2.57 Post pandemic, May through December 2020, average daily minutes spent communication with friends via texting. phone calls and video chats N Min Q1 Median Q3 Max Mean St Dev 44,328 2.23 6.25 9.23 11.56 29.29 9.86 2.27 The Questions '1. What is the maximum a person could spend daily communicating with friends preApandemic and still be less than 25% ofall the other people's average daily communication that year? 2. The dataset for PreApandemic, May through December 2019. average daily minutes spent communication with friends via texting. phone calls and video chats has a Q1 of 5.22. Explain what this means in terms of the average daily commucation with friends in minutes of the 44, 328 people in the dataset. 3. Does the dataset for Post pandemic, May through December 2020, average daily minutes spent communication with friends via texting, phone calls and video chats appear to be symmetrical or skewed? Use statistical evidence from the numerical summary to justify your answer. 4. What would happen to the mean of the dataset if an additional point was added at or greater than the maximum value? Why? 5. What would happen to the standard deviation of the dataset if an additional point was added at or less than the minimum value? Why? 6. Which of these datasets appears to be more skewed? Use a statistical analysis to justify your answer. Edit View Insert Format Tools Table 12ptv ParagraphVI B I U iv £v Tzvl 09v av Ed's!" @v' E a [$5 I Ev EEV g
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1. 9.25mins
2. Among 44,328 people, 25%or11,082 spend less than Q1(5.22mins) in average daily communication.
3. Symmetrical
4. The mean will be higher
5. The standard deviation will be higher
6. Data set for pre-pandemic is more skewed.
Step-by-step explanation
1.
In this question, we are concerned with Q3 or the upper quartile. It is the value that is greater than 75% of values in a data set. It means that 25% of values in the data set is greater than Q3.
Q3=9.25
It means that 25% of all the other people's average daily communication during pre-pandemic is greater than 9.25mins
2.
Q1 or the lower quartile is the value that is greater than 25% of values in a data set. It means that among 44,328 people, 25%or11,082 spend less than Q1(5.22mins) in average daily communication.
3.
Skewness is the measure of symmetry of a given data set. It is said to be perfectly symmetrical if skewness is equal to zero. The easiest way to estimate skewness is using the formula
Sk=Standarddeviation3×(Mean−Median)?
For post pandemic:
Sk=2.273×(9.86−9.23)?
Sk=0.833
Since the value is close to zero, the data is approximately symmetrical.
4.
Since the mean is the average of all values in a data set, the mean will be higher if an additional point was added at or greater than the maximum value.
5.
Since the standard deviation is the measure of average deviation of data from the mean, the standard deviation will be higher if an additional point was added at or less than the minimum value.
6.
From #3, it was calculated that for post pandemic, Sk=0.833
For pre-pandemic:
Sk=Standarddeviation3×(Mean−Median)?
Sk=2.573×(7.86−6.78)?
Sk=1.261
Since the skewness is higher for pre-pandemic, it can be concluded that data set for pre-pandemic is more skewed.
