Answer:
x = 5
Step-by-step explanation:
Mode: The most frequently occurring data value.
Median: The middle value when all data values are placed in order of size.
Mean: The sum of all data values divided by the total number of data values.
As the mode is the most frequently occurring data value, x must be 3, 4, 5 or 8.
If the mode is 3 or 4, then the data set will be {3, 3, 4, 5, 8} or {3, 4, 4, 5, 8}. Therefore, the median would be 4.
If the mode is 5 or 8, then the data set will be {3, 4, 5, 5, 8} or {3, 4, 5, 8, 8}. Therefore, the median would be 5.
Therefore, the median is 4 or 5.
[tex]\boxed{\sf mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}}[/tex]
If x = 4, the mean would be:
[tex]\sf \implies mean=\dfrac{3+4+5+8+4}{5}=\dfrac{24}{5}=4.8[/tex]
If x = 5, the mean would be:
[tex]\sf \implies =\dfrac{3+4+5+8+5}{5}=\dfrac{25}{5}=5[/tex]
Therefore, the only value of x that allows the mean, median and mode to all have the same value is x = 5.