The five month moving averages for the following data Month (rth)4344…

The correct answer is Option (1) → 109, 112.2, 117, 120.6, 126

A five-month moving average is the mean of five consecutive values; each new average drops the oldest month and adds the next one. Nine months give 9 − 5 + 1 = 5 averages:

    \(\text{Months 43 to 47: } 105 + 106 + 110 + 110 + 114 = 545,\quad 545 \div 5 = 109\)
    \(\text{Months 44 to 48: } 545 - 105 + 121 = 561,\quad 561 \div 5 = 112.2\)
    \(\text{Months 45 to 49: } 561 - 106 + 130 = 585,\quad 585 \div 5 = 117\)
    \(\text{Months 46 to 50: } 585 - 110 + 128 = 603,\quad 603 \div 5 = 120.6\)
    \(\text{Months 47 to 51: } 603 - 110 + 137 = 630,\quad 630 \div 5 = 126\)

So the moving averages are 109, 112.2, 117, 120.6 and 126.