IIFT 2017 Question Paper

Quarters with negative deviation from its trend

Average deviation for any quarter  = Sum of all deviations from the quarter / Number of years

By observation, Quarter 1 will be rejected as all its deviations are positive.

Average deviation for quarter 2  =  ((63-64.5) + (59-61.12) + (55-55.25))/3 = (-1.5-2.12-0.25)/3 = -3.87/3

Average deviation for quarter 3  =  ((56-60.38) + (63-65.5) + (56-58))/3 = (-4.38-2.5-2)/3 = -8.88/3

Average deviation for quarter 4 =   ((61-61.38) + (67-65.25) + ( 52-56.25 ))/3 = (-0.38+1.75-4.25)/3 = -2.88/3

Quarter 3 has maximum average negative deviation.

Compound Average Growth Rate= $$[\frac{End value}{Startvalue}]^{1/n}-1$$

1998 growth rate = $$[\frac{61}{65}]^{1/4}-1$$= -1.57%

1999 growth rate = $$[\frac{67}{68}]^{1/4}-1$$  = -0.36%

2000 growth rate = $$[\frac{52}{70}]^{1/4}-1$$  = -7.4%

2001  growth rate = $$[\frac{58}{60}]^{1/4}-1$$  = -0.84%

1998 is the year with second lowest quarterly CAGR.

Value of output for year 

1998      65+58+56+61 = 240

1999      68+63+63+67 = 261

2000      70+59+56+52 = 237

2001      60+55+51+58 = 224

Output Growth for

1999       ((261-240)/240)*100 = 8.75

2000       ((237-261)/261)*100  = -9.2

2001        ((224-237)/237)*100  = 5.48

To calculate the number of times graphs intersects, we can check number of times the difference of the two values changes sign. 

We can also plot a graph to calculate number of times they intersect.

Trend curve insects output curve 6 times.

Check the number of times where the difference of the actual value and trend value change sign.