Answered: View attached photo (commuting times)…

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

*View attached photo (commuting times) and answer the following questions. TY!*

The commuting times (in minutes) of randomly selected employees at Neiman Marcus are recorded in the attached photo.

A) Construct a histogram for commuting times and describe the shape of the distribution.

B)Construct a box-and-whisker plot and then compares it to your histogram in Part A.

C)Find the skewness and kurtosis of commuting times. Does your results support your observation in part a and b.

Commuting Times (in minutes)
20
45
90
15
40
150
120
40
60
80
80
60
30
90
60
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
120
120
200
10
65
40
60
60
120
140

Expert Solution

Step 1

Introduction -

Histogram - A histogram is a graphical representation that organize a a group of data points into user-specified ranges . Similar in appearance to a bar graph , the histogram condenses a data series into an easily interpreted visual by taking many data pints them into logical or bins .

Box and whisker plot - In descriptive statistics , a box or boxplot ( also known as box and whisker plot ) is a type of chart often used in explanatory data analysis . Box plot visually show the distribution of numerical data and skewness through displaying the data quartile or percentile and averages .

Box plots show the five -number summary of a set of data including the minimum score , first lower quartile , median , third upper quartile , and maximum score .

Skewness and Kurtosis -

$S k e w n e s s = \frac{1}{N} \sum_{} {[\frac{(X_{i} - X)}{σ}]}^{3} K u r t o s i s = \frac{1}{N} \sum_{} {[\frac{(X_{i} - X)}{σ}]}^{4}$

$w h e r e, N = t o t a l f r e q u e n c y x = m e a n σ = S \tan d a r d d e v i a t i o n$

$M e a n = \frac{s u m o f o b s e r v a t i o n s}{t o t a l o b s e r v a t i o n s} S \tan d a r d d e v i a t i o n = \sqrt{\frac{{(X_{i} - X)}^{}}{N}}$