Respuesta :
Answer: The distribution of the data set is positively skewed.
Explanation:
In order to see whether the given data set is symmetric, positively skewed or negatively skewed, we will find the mean, median and mode of the given data set.
For symmetric distribution, [tex]Mean = Median=Mode[/tex]
For positively skewed distribution, [tex]Mean > Median>Mode[/tex]
For negatively skewed distribution, [tex]Mean < Median<Mode[/tex]
The mean of the given data set is given below:
[tex]Mean = \frac{27+23+22+38+43+24+25+23+22+54+31+30+29+48+27+25+29+28+26+33+25+21+23+34+20+23}{26}[/tex]
[tex]=\frac{753}{26}[/tex]
[tex]=28.96[/tex]
Now, the Median is:
To find the median we need to sort the data in ascending order as:
[tex]20,21,22,22,23,23,23,23,24,25,25,25,26,27,27,28,29,29,30,31,33,34,38,43,48,54[/tex]
[tex]Median=\left(\frac{N+1}{2} \right)^{th} item[/tex]
[tex]=\left(\frac{26+1}{2}\right)^{th} item[/tex]
[tex]=13.5^{th} item[/tex]
[tex]=26+0.5 \times (27-26)[/tex]
[tex]=26.5[/tex]
[tex]\therefore Median = 26.5[/tex]
The mode is the most frequently occurring observation. Therefore the mode is:
[tex]Mode=23[/tex]
Since the [tex]Mean >Median>Mode[/tex], therefore the distribution of the given data set is positively skewed.
