Question

Question in attachment

Answer 1

The range within 1 standard deviation :155.12 ,328.38

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 =(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{((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