CityTime (minutes)Rome24.9Milan26.8Naples26.2Turin28.1Palermo31.7Genoa25.8Bologna23.3Florence32.1Bari28.5Catania24.4Verona29.3Venice24.8Messina38.1Padua28.3Trieste28.4Taranto24.6Prato20.1Modena23.4 a) What is the mean commute time for these 18 cities? b) What is the median commute time for these 18 cities? c) What is the mode for these 18 cities? d) What is the variance and standard deviation of commute times for these 18 cities? e) Find the z – score value of commute time for these 18 cities. f) Find 28th and 77th Percentile of commute times for these 18 cities.

Answered: a) What is the mean commute time…

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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City	Time (minutes)
Rome	24.9
Milan	26.8
Naples	26.2
Turin	28.1
Palermo	31.7
Genoa	25.8
Bologna	23.3
Florence	32.1
Bari	28.5
Catania	24.4
Verona	29.3
Venice	24.8
Messina	38.1
Padua	28.3
Trieste	28.4
Taranto	24.6
Prato	20.1
Modena	23.4

a) What is the mean commute time for these 18 cities?
b) What is the median commute time for these 18 cities?
c) What is the mode for these 18 cities?
d) What is the variance and standard deviation of commute times for these 18 cities?
e) Find the z – score value of commute time for these 18 cities.
f) Find 28^th and 77^th Percentile of commute times for these 18 cities.

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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Step 1

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The mean commute time for these 18 cities is,

$\begin{array}{rcl} M e a n & = & \frac{\sum_{} X}{n} \\ = & \frac{24.9 + 26.8 + 26.2 + 28.1 + 31.7 + 25.8 + 23.3 + 32.1 + 28.5 + 24.4 + 29.3 + 24.8 + 38.1 + 28.3 + 28.4 + 24.6 + 20.1 + 23.4}{18} \\ = & \frac{488.8}{18} \\ = & 27.1556 \end{array}$

Thus, the mean commute time for these 18 cities is 27.1556.

Step 2

The data in the ascending order is 20.1, 23.3, 23.4, 24.4, 24.6, 24.8, 24.9, 25.8, 26.2, 26.8, 28.1, 28.3, 28.4, 28.5, 29.3, 31.7, 32.1, and 38.1.

For even data set, the median is the average of ${(\frac{n}{2})}^{t h}$ and ${(\frac{n}{2} + 1)}^{t h}$ observation.

The sample size is 18, than the median is the average of 9^th temperature and 10^th temperature. The median commute time for these 18 cities is,

$\begin{array}{rcl} M e d i a n & = & \frac{26.2 + 26.8}{2} \\ = & \frac{53}{2} \\ = & 26.5 \end{array}$

Thus, the median commute time for these 18 cities is 26.5.

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