The histogram of the variable below shows that the distribution of values is fairly symmetric. Which is most likely in this case (and in other cases where you have a symmetric distribution)?0.20Density0.15102O The median is greater than the mean.O The mean is greater than the median.O The mean and median are likely equal.0.100.050.006810

Answered: he histogram of the variable below…

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

The histogram of the variable below shows that the distribution of values is fairly symmetric. Which is most likely in this case (and in other cases where you have a symmetric distribution)?
0.20
Density
0.15
1
0
2
O The median is greater than the mean.
O The mean is greater than the median.
O The mean and median are likely equal.
0.10
0.05
0.00
6
8
10

Expert Solution

Step 1

For a symmetric distribution, the mean and median are equal. This is because in a symmetric distribution, the data is evenly distributed around the central point, so the average value (mean) and the middle value (median) are the same.

However, it's important to note that not all distributions have this property. For example, in a skewed distribution, the mean can be pulled in the direction of the long tail, while the median remains closer to the center of the distribution. In such cases, the mean and median will be different.