Respuesta :
Answer:
"The mean is equal to the median, so the data is symmetrical" is the correct relationship between the mean and median about the shape of the data.
Step-by-step explanation:
As the table is given by
10 5 8 10 12 6
8 10 15 6 12 18
So fetching the data from the table
10 5 8 10 12 6 8 10 15 6 12 18
Calculating the mean
[tex]Mean= \frac{10+5+8+10+12+6+8+10+15+6+12+18}{12}[/tex]
[tex]Mean= 10[/tex]
Rearranging the data in ascending order will be
5 6 6 8 8 10 10 10 12 12 15 18
Calculating the median
[tex]Median=\frac{(\frac{n}{2})th+(\frac{n}{2}+1)th}{2}=\frac{10+10}{2}=10[/tex]
As we can that
[tex]Mean = Median[/tex]
So, we can conclude that as the mean is equal to the median, so the data is symmetrical.
Therefore, "The mean is equal to the median, so the data is symmetrical" is the correct relationship between the mean and median about the shape of the data.
Keywords: data distribution, median , mean, symmetrical data
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Answer:
The mean is equal to the median, so the data is symmetrical.
Step-by-step explanation:
The given table is
First row: 10, 5, 8, 10, 12, 6.
Second row: 8, 10, 15, 6, 12, 18.
To find the right answer, we need to calculate the mean the the median of this data set.
[tex]x=\frac{\sum x_{i} }{N}=\frac{10+5+8+10+12+6+8+10+15+6+12+18}{12}=\frac{120}{12}=10[/tex]
The mean of the data set is 10.
Now, to find the median, first, we need to arrange the data set from least to greatest.
5, 6, 6, 8, 8, 10, 10, 10, 12, 12, 15, 18.
Notice that the middle is between 10 and 10,
[tex]Me=\frac{10+10}{2}=10[/tex]
Therefore, the median and the mean are equal, both are equal to 10.
When this happens, it means the data set is symmetrical, its box plots would be symmetrical. So, the right answer is the third choice.
