1. Table 4 values shows a Linear function.
2. 6 seconds faster were the runner in Group 2 than runners in Group 1.
Linear function are those which are in the form of f(x) = x ( here the line is passing through the origin )
Also Linear function can be in the form of y = mx + c where 'm' is the slope of the given line and 'c' is constant.
1. In the table 4 we conclude that:
y = f(x)
f(2) = 4 -------- point is ( 2, 4)
f(4) = 6 -------- point is ( 4, 6)
f(6) = 8 -------- point is ( 6, 8)
f(8) = 10 -------- point is ( 8, 10)
for the points to be in a line their slope must be equal:
Slope of line from point (2, 4) and (4, 6):
Slope = ( y2 - y1 )/ (x2 - x1)
Slope = ( 6 - 4 )/(4-2)
Slope = 2/2 = 1
Similarly,
Slope of line from point (4, 6) and (6, 8):
Slope = ( 8- 6 )/(6-4)
Slope = 1
Same as for points (6, 8) and (8,10)
Slope = 1
here the slop of the all points are same, so they lie on a single line and forms a linear equation in form of y = mx + c.
Hence, Table 4 values shows a Linear function.
2. Here we have given the data:
For group 1: 55 68 64 66 70
For group 2: 56 58 59 61 57
Average or Geometric mean :
Sum of all the observation / number of observation
Average for Group 1 = ( 55 + 68 +64 +66 + 70)/5
Average for Group 1 = 64.6
Average for Group 2 = (56 + 58 + 59 + 61 + 57)/5
Average for Group 2 = 58.2
Difference between the Average of group 1 and group 2: 6.4.
in whole number 6 seconds.
Hence,
6 seconds faster were the runner in Group 2 than the runners in Group 1.
Learn more about " Arithmetic Mean " from here: https://brainly.com/question/15196910
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