Answered: b) Exhibit 2 shows the histogram and…

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

b) Exhibit 2 shows the histogram and Exhibit 3 gives a table of summary statistics for the individual’s age of those included in the data.

i) From Exhibit 2, with examples, provide three essential items that could improve the above chart.

ii) From Exhibit 3, What is the median value and how do you obtain it.

iii) From the answer you provided in part (ii) and based on Exhibit 2 and Exhibit 3, describe the shape of the distribution of this data. Give some intuitive explanation for why this data produces this shape.

c) Use Exhibit 3 to interpret in context the central tendency of the smoker’s “Age”.

d) i) Write down the formula for the sample standard deviation and using the sample variance from Exhibit 3 calculate the standard deviation value.

Show all workings.

ii) Other measures of the spread/dispersion of the data are the Range, Interquartile Range and Coefficient of Variation. From Exhibit 3, calculate the

Range
IQR, and
CV

Give interpretations for any 2 of the 3 values.

35.0%
30.0%
25.0%
20.0%
15.0%
10.0%
5.0%
0.0%
Exhibit 2
15-29 30-44 45-59 60-74
75-89 90-105
Statistics
Mean
Standard Error
Mode
Standard Deviation
Sample Variance
Range
Minimum
Maximum
Count
First Quartile
Second Quartile
Third Quartile
Exhibit 3
Interquartile Range (IQR)
Coefficient of Variation (CV)
Individual age
49.61
0.47
40
18.44
340.21
81
16
97
1565
34
47
65
31
37.18%

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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