4. Braking Distance. The variable Braking Distance in the Cars2020 dataset gives braking distance in feet for new car models in 2020. a. Use Statkey to generate a dotplot of this variable. Describe the shape of the distribution here. Include a screen shot of your dotplot with summary statistics. b. Find the mean, the standard deviation, and the five number summary for the data in this variable. Write them below. i. Mean: ii. Standard Deviation: iii. Five Number Summary: IQR: c. Calculate the IQR. d. Determine by hand using the IQR method whether there are any outliers. Show all calculations, and list the outliers, if any.
4. Braking Distance. The variable Braking Distance in the Cars2020 dataset gives braking distance in feet for new car models in 2020. a. Use Statkey to generate a dotplot of this variable. Describe the shape of the distribution here. Include a screen shot of your dotplot with summary statistics. b. Find the mean, the standard deviation, and the five number summary for the data in this variable. Write them below. i. Mean: ii. Standard Deviation: iii. Five Number Summary: IQR: c. Calculate the IQR. d. Determine by hand using the IQR method whether there are any outliers. Show all calculations, and list the outliers, if any.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
I have provided the dot plot below, please only answer the highlighted questions
![### Braking Distance Analysis
The variable **Braking Distance** in the *Cars2020* dataset provides the braking distances (in feet) for new car models in the year 2020.
#### Instructions:
1. **Generate a Dotplot:**
Use Statkey to create a dotplot of the braking distance variable. Provide a screenshot of your dotplot along with the summary statistics. Describe the shape of the distribution based on the dotplot.
2. **Calculate Descriptive Statistics:**
a. **Mean:**
Write down the mean braking distance.
b. **Standard Deviation:**
Calculate and note the standard deviation of the braking distances.
c. **Five Number Summary:**
Determine and list the five-number summary for the braking distance data. The five-number summary consists of:
- Minimum
- First Quartile (Q1)
- Median
- Third Quartile (Q3)
- Maximum
3. **Calculate the Interquartile Range (IQR):**
Compute the IQR for the braking distances using the formula:
\[
\text{IQR} = Q3 - Q1
\]
4. **Outlier Detection Using IQR Method:**
Determine if there are any outliers in the data using the IQR method. Show all calculations and list any outliers found. The steps for finding outliers using the IQR method are:
- Calculate the lower bound: \( Q1 - 1.5 \times IQR \)
- Calculate the upper bound: \( Q3 + 1.5 \times IQR \)
Any data point below the lower bound or above the upper bound is considered an outlier.
This exercise aims to apply statistical methods to analyze the braking distance of new 2020 car models, helping in understanding data distribution, central tendency, and variability.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe88a8cea-da71-40ab-aaed-a0e0afa0772e%2Fefb1e781-65ae-448d-918e-9ab085d7ba1c%2Fjx4xxv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Braking Distance Analysis
The variable **Braking Distance** in the *Cars2020* dataset provides the braking distances (in feet) for new car models in the year 2020.
#### Instructions:
1. **Generate a Dotplot:**
Use Statkey to create a dotplot of the braking distance variable. Provide a screenshot of your dotplot along with the summary statistics. Describe the shape of the distribution based on the dotplot.
2. **Calculate Descriptive Statistics:**
a. **Mean:**
Write down the mean braking distance.
b. **Standard Deviation:**
Calculate and note the standard deviation of the braking distances.
c. **Five Number Summary:**
Determine and list the five-number summary for the braking distance data. The five-number summary consists of:
- Minimum
- First Quartile (Q1)
- Median
- Third Quartile (Q3)
- Maximum
3. **Calculate the Interquartile Range (IQR):**
Compute the IQR for the braking distances using the formula:
\[
\text{IQR} = Q3 - Q1
\]
4. **Outlier Detection Using IQR Method:**
Determine if there are any outliers in the data using the IQR method. Show all calculations and list any outliers found. The steps for finding outliers using the IQR method are:
- Calculate the lower bound: \( Q1 - 1.5 \times IQR \)
- Calculate the upper bound: \( Q3 + 1.5 \times IQR \)
Any data point below the lower bound or above the upper bound is considered an outlier.
This exercise aims to apply statistical methods to analyze the braking distance of new 2020 car models, helping in understanding data distribution, central tendency, and variability.
Transcribed Image Text:### Dotplot Analysis of Braking Data
#### Graph Description:
The image above presents a dotplot, which is a type of statistical chart used to display frequency counts of individual data points. In this case, the dotplot visualizes braking data.
#### X-Axis:
The x-axis (horizontal axis) represents the braking distances, ranging from 110 to 145. Each distinct value on the x-axis corresponds to a specific braking measurement.
#### Y-Axis:
The y-axis (vertical axis) represents the frequency count of occurrences for each braking distance value, extending from 0 to 50. Each dot above a specific value on the x-axis indicates a single instance where that braking distance was recorded.
#### Data Points:
- The braking distances show variability, with the highest concentrations occurring between approximately 125 to 140.
- This range has multiple dots stacked at various points, suggesting that these distances are more common in the dataset.
- Notably, there are fewer data points on the lower end (110-120) and higher end (141-145) of the x-axis.
#### Interpretation:
The dotplot is particularly useful for identifying clusters and gaps in the dataset. For instance:
- There is a significant clustering of data points between 125 and 140, indicating that most braking distances fall within this range.
- The frequency of braking distances drops off significantly beyond this interval, highlighting less common occurrences of extremely high or low braking distances.
This visualization is part of a set that includes both a histogram and a box plot, as indicated by the tabs on top of the graph. The currently displayed dotplot provides a straightforward method to visually assess the distribution and frequency of braking distances in the dataset.
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