Answered: Grade (x) da Number of Students (f)to…

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

Find the mean, median, and mode grade of 42 students in Math 1 whose grades are in the following distributions. please show work. This problem deals with statistics, "Choosing a Measure of Central Tendency."

Grade (x)
dn Number of Students (f)o otud fxd v CF<
93 Meesl)
(1esuper
alsvisinl ea
90
88
5.
85
83
4.
80
6.
77
7.
75
11
57
2.
2.
4.

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.

Expert Solution

Step 1

Mean is the average value of a random variable which is computed by $μ = \frac{\sum f \cdot x}{\sum f}$ , where x is random variable and f is frequency. The frequency for a value of random variable represents the number of times the value is repeated in the dataset.

The median is the value which lies in the middle of the dataset or which divides the dataset into two equal parts when arranged in ascending order. The mode is the value which is repeated most that is the value with highest frequency.