Question

Question in attachment

Answer 1

Answer:

The range within 1 standard deviation :155.12 ,328.38

Step-by-step explanation:

Data: 338+160+210+180+166+272+128+409+240+250+160+300+340+200+194+132+202+180+420+380+325+185+233+198

$Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}$

$Mean =\frac{338+160+210+180+166+272+.........+233+198}{24}$

Mean =241.75

$\text{Standard deviation} = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}$

Standard deviation = $\sqrt{\frac{(338-241.75)^{2}+(160-241.75)^{2}+......+(185-241.75)^{2}+(233-241.75)^{2}+(198-241.75)^{2}}{24-1}}$

Standard deviation =86.63

Range within 1 standard deviation :$(\mu-\sigma,\mu+\sigma)$

Range within 1 standard deviation :(241.75-86.63,241.75+86.63)

Range within 1 standard deviation :155.12 ,328.38

Hence The range within 1 standard deviation :155.12 ,328.38