Develop a 3-week moving average for the following time series Time PeriodTime Series Value 19 22 39 416 511 62 77 Find the value for MSE. Round your calculations to 2 decimal places.

MSE = 198.18 / 3 = 66.06

Step-by-step explanation:

Time period : Time series value

           1        :   9

           2       :    2

           3       :    9

           4       :    16

           5       :    11

           6       :    2

           7       :     7

3  weeks moving average

F4 = average of weeks 1-3 = ( 9 + 2 + 9 ) / 3 = 20 / 3 = 6.67

F4 = average of weeks 2-4 = ( 2 + 9 + 16 ) / 3 = 27 / 3 = 9

F4 = average of weeks 3-5 = ( 9 + 16 + 11 ) / 3 = 36 / 3 = 12

F4 = average of weeks 4 - 6 = ( 16 + 11 + 2 ) / 3 = 9.67

attached is the table showing the development of the 3-week moving average

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this