Given the data as shown in the table:
Range = max - min = 28 - 20 = 8
The mean of the data = Sum/number
The sum of the data = 20 + 22 * 4 + 28 * 2 = 164
The number of the data = 1 + 4 + 2 = 7
So, the mean of the data = 164/7 = 23.43
The standard deviation will be :
[tex]\sqrt[]{\frac{\sum ^{}_{}(x-\operatorname{mean})^2}{n-1}}[/tex]The numerator =
[tex](20-23.43)^2+4\cdot(22-23.43)^2+2\cdot(28-23.43)^2=61.714[/tex]So, the standard deviation =
[tex]\sqrt[]{\frac{61.714}{7-1}}=\sqrt[]{\frac{61.714}{6}}=3.207[/tex]So,
range = 8
mean = 23.43
SD = 3.207
So,
The answer is: option (2) : range < mean