The force acting on a beam was measured 5 times under the same operating conditions. This process was repeated by 3 observers, resulting in 3 sets of data. The standard deviations of these data sets were: Standard Deviation 1= 1.11, Standard Deviation 2= 0.99, Standard Deviation 3= 1.15 The corresponding mean values were: 52.3, 51.5, and 52.7, respectively. Compute the Pooled Standard Deviation for these data sets. (Provide your answer using two decimal places)

The Pooled Standard Deviation for these data sets is 1.09

Step-by-step explanation:  

Given that;

Standard Deviation 1 = 1.11

Standard Deviation 2 = 0.99

Standard Deviation 3 = 1.15

pooled standard deviation is given as;

= (n1 - 1 )s1² + ..... + ( nk - 1 )sk² / n1 + ..... + nk - 1

where n1, n2....., nk are the sample sizes of k groups and s1, s2, ....., sk are the standard deviations of k groups respectively

so for the 3 groups;

² =   (n1 - 1 )s1² + (n2 - 1 )s2² + ( n3 - 1)s3² / n1 + n2 + n3 - 3

we substitute

² =   (5 - 1 )1.11² + (5 - 1 )0.99 ² + ( 5 - 1)1.15² / 5 + 5 + 5 - 3

² =   (4.9284 + 3.9204 + 5.29) / 12

² =   14.1388 / 12

² =   1.1782

= √1.1782

= 1.08544 ≈ 1.09

Therefore, The Pooled Standard Deviation for these data sets is 1.09

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,