Respuesta :
Given:
The data set is:
14, 15, 3, 15, 14, 14, 18, 15, 8, 16
To find:
The mean, median and mode of the given data set.
Solution:
We have,
14, 15, 3, 15, 14, 14, 18, 15, 8, 16
Arrange the data values in ascending order.
3, 8, 14, 14, 14, 15, 15, 15, 16, 18
Mean of the data set is:
[tex]Mean=\dfrac{\text{Sum of all observations}}{\text{Number of observation}}[/tex]
[tex]Mean=\dfrac{3+8+14+14+14+15+15+15+16+18}{10}[/tex]
[tex]Mean=\dfrac{132}{10}[/tex]
[tex]Mean=13.2[/tex]
The number of observation is 10 which is an even number. So, the median of the data set is:
[tex]Median=\dfrac{(\dfrac{n}{2})\text{th term}+(\dfrac{n}{2}+1)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{(\dfrac{10}{2})\text{th term}+(\dfrac{10}{2}+1)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{5\text{th term}+6\text{th term}}{2}[/tex]
[tex]Median=\dfrac{14+15}{2}[/tex]
[tex]Median=\dfrac{29}{2}[/tex]
[tex]Median=14.5[/tex]
Mode is the most frequent value of the data set.
In the given data set the highest frequency is 3 because 14 and 15 occurs three times.
So, the mode of the given data set is 14 and`15.
Therefore, the mean is 13.2, median is 14.5 and mode is 14 and 15.
