Answer:
Mean is [tex]\overline{x} =15.4[/tex] and standard deviation is 3.02581485
Step-by-step explanation:
Given mean is 19.4 and standard deviation is 5.8
the given data are: - 12, 15, 17, 20, 13, 11, 18, 19, 15, 14
Mean of given data is calculated as :-
[tex]\overline{x} =\frac{1}{n}\sum_{i=1}^{n}x[/tex]
[tex]\overline{x} =\frac{12+15+17+20+13+11+18+19+15+14}{10}[/tex]
[tex]\overline{x} =\frac{12+15+17+20+13+11+18+19+15+14}{10}[/tex]
[tex]\overline{x} =\frac{154}{10}[/tex]
[tex]\overline{x} =15.4[/tex]
Mean is [tex]\overline{x} =15.4[/tex]
standard deviation is calculated as :-
[tex]s=\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x-\overline{x})^{2}[/tex]
the sum of [tex](x-\overline{x})^{2}[/tex] is performed in figure-1
[tex]s=\sqrt{\frac{1}{10-1}\sum_{i=1}^{n}(\frac{412}{5})[/tex]
[tex]s=\sqrt{\frac{1}{9}\times\frac{412}{5}[/tex]
[tex]s=\sqrt{(\frac{412}{45})[/tex]
[tex]s=\sqrt{(\frac{412}{45})[/tex]
[tex]s=3.02581485[/tex]
standard deviation is 3.02581485
