View the attatchments and then explain the following - Find the skewness and kurtosis of commuting times and explain what the box and whisker plot and data is showing or explaining.

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View the attatchments and then explain the following

- Find the skewness and kurtosis of commuting times and explain what the box and whisker plot and data is showing or explaining.

**Commuting Times (in minutes) Data Analysis**

The dataset consists of commuting times measured in minutes. Here are some key statistical measures derived from the data:

- **Minimum**: 10 minutes
- **First Quartile (Q1)**: 40 minutes
- **Median**: 60 minutes
- **Third Quartile (Q3)**: 120 minutes
- **Maximum**: 260 minutes
- **Mean**: 73.74 minutes

**Box Plot Explanation:**

The accompanying box plot provides a visual representation of the distribution of commuting times:

- **Box**: The central box represents the interquartile range (IQR), which contains the middle 50% of the data (from Q1 to Q3). For this dataset, it ranges from 40 to 120 minutes.
- **Median Line**: Inside the box, a line indicates the median at 60 minutes, showcasing where the center of the data lies.
- **Whiskers**: The whiskers extend to the smallest and largest values within 1.5 times the IQR from Q1 and Q3, respectively. The lower whisker bottoms at 10 minutes.
- **Outliers**: Any data points beyond the whiskers are considered outliers. In this plot, the dot above the upper whisker at 260 minutes represents an outlier, indicating a significantly longer commuting time compared to most of the data.

This box plot is a helpful tool for quickly visualizing the distribution, central tendency, and variability of commuting times in the dataset, as well as identifying any potential outliers.
Transcribed Image Text:**Commuting Times (in minutes) Data Analysis** The dataset consists of commuting times measured in minutes. Here are some key statistical measures derived from the data: - **Minimum**: 10 minutes - **First Quartile (Q1)**: 40 minutes - **Median**: 60 minutes - **Third Quartile (Q3)**: 120 minutes - **Maximum**: 260 minutes - **Mean**: 73.74 minutes **Box Plot Explanation:** The accompanying box plot provides a visual representation of the distribution of commuting times: - **Box**: The central box represents the interquartile range (IQR), which contains the middle 50% of the data (from Q1 to Q3). For this dataset, it ranges from 40 to 120 minutes. - **Median Line**: Inside the box, a line indicates the median at 60 minutes, showcasing where the center of the data lies. - **Whiskers**: The whiskers extend to the smallest and largest values within 1.5 times the IQR from Q1 and Q3, respectively. The lower whisker bottoms at 10 minutes. - **Outliers**: Any data points beyond the whiskers are considered outliers. In this plot, the dot above the upper whisker at 260 minutes represents an outlier, indicating a significantly longer commuting time compared to most of the data. This box plot is a helpful tool for quickly visualizing the distribution, central tendency, and variability of commuting times in the dataset, as well as identifying any potential outliers.
**Commuting Times (in minutes)**

20  
45  
90  
15  
40  
150  
120  
40  
60  
80  
80  
60  
30  
90  
60  
30  
30  
260  
120  
120  
30  
30  
90  
10  
120  
120  
45  
60  
12  
80  
50  
40  
120  
50  
30  
40  
60  
45  
120  
50  
40  
40  
120  
120  
200  
10  
65  
40  
60  
60  
120  
140
Transcribed Image Text:**Commuting Times (in minutes)** 20 45 90 15 40 150 120 40 60 80 80 60 30 90 60 30 30 260 120 120 30 30 90 10 120 120 45 60 12 80 50 40 120 50 30 40 60 45 120 50 40 40 120 120 200 10 65 40 60 60 120 140
Expert Solution
Step 1

Given data of commuting times
Statistics homework question answer, step 1, image 1

Using this data we can use excel functions =Skew() to find skewness and =KURT() to find kurtosis 

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