Frequency 20 Vehicle Speeds through a Construction Zone 25 Frequency 30 35 Speeds vari 40 Five new data values were added to the data set. Histogram for the new data is given below. 45 60 Based on the histogram, which measure of central tendency (the mean or median), better represents the center of the updated data set?
Frequency 20 Vehicle Speeds through a Construction Zone 25 Frequency 30 35 Speeds vari 40 Five new data values were added to the data set. Histogram for the new data is given below. 45 60 Based on the histogram, which measure of central tendency (the mean or median), better represents the center of the updated data set?
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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Transcribed Image Text:### Vehicle Speeds through a Construction Zone
The first image is a histogram displaying the frequency of vehicle speeds through a construction zone. The horizontal axis represents speed ranges (in units that appear to be in miles per hour), and the vertical axis represents frequency. The speed ranges are divided into intervals: 20-25, 25-30, 30-35, 35-40, and 40-45. The frequency of vehicles in each interval is as follows:
- 20-25: Frequency of 2
- 25-30: Frequency of 3
- 30-35: Frequency of 4
- 35-40: Frequency of 3
- 40-45: Frequency of 2
The histogram displays a peak at the 30-35 interval, indicating that the most common vehicular speed falls within this range.
### New Data Histogram
The second image shows a histogram for the updated data set after five new data values were added. The x-axis represents the speed ranges, labeled as "var1," and the y-axis represents frequency. The speed intervals are the same as the first histogram, with an additional interval (45-50).
- 20-25: Frequency of 2
- 25-30: Frequency of 3
- 30-35: Frequency of 4
- 35-40: Frequency of 3
- 40-45: Frequency of 2
- 45-50: Not shown
The additional data do not alter the peak of the distribution significantly; the frequency at the 30-35 interval remains the highest.
### Analysis
Based on the histograms, consider whether the mean or median better represents the center of the updated data set. Since the distribution displays a symmetrical bell shape centered at the 30-35 interval, the mean and median are likely close or coinciding. However, the median may sometimes better capture the central tendency if outliers impact the mean in an extended data set.
Expert Solution
Step 1: Describing histogram
The histogram is a graphical representation of the distribution of numerical data.
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