Arithmetic mean of nine observations is calculated as 38. But in doing so, mistakenlythe observation 27 is taken instead of 72. Find the actual mean of the data.​

Actual Mean = 43

Step-by-step explanation:

Given Mean = 38

No of observations = 9

we know,

Mean = Sum / N

38 = Sum/ 9

Sum = 38 x 9 = 342

Since the observation 27 was mistakenly taken instead of 72, we subtract 27 from the sum and add 72.

New sum = 342 - 27 = 315 again, 315 + 72 = 387

The no. of observations stays the same.

Actual mean = New Sum / N

= 387/9

=43

Step-by-step explanation:

arithmetic mean =38

n=9

mean=sum/n

sum=mean×n=38×9=342

mistakenly observation 27 is taken instead of 72

new sum becomes =342+72-27=387

now

new mean =new sum/n=387/9=43

the actual mean of the data is 43.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."