The shape of the distribution, is symmetric, is the best description of statistics about scores.
What is standard deviation ?
The standard deviation is the positive square root of the variance of this data set. Variance of a data set is the sum of squared differences of the data values from its mean to the total count of data values.
The given data in the problem is;
Mean = 78%
Standard deviation = 4%
Min = 64
Median = 78
Q1 = 72
Q3 = 84
Max = 99
The condition for the symmetric distribution is found as;
[tex](\rm Q_2-Q_1)=Q_3-Q_2)[/tex]
From the data we have;
[tex](\rm Q_2-Q_1)=Q_3-Q_2)\\\\ (\rm Q_2-Q_1)= (\rm 84-78)= 6 \\\\ Q_3-Q_2)=(78-72) = 6 \\\\[/tex]
So that , [tex](\rm Q_2-Q_1)=Q_3-Q_2)[/tex].
Hence, the condition of symmetry is followed.
To learn more about the symmetry, refer to the link;l
https://brainly.com/question/15970176
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