5 Marks Questions

Question 15 Marks

Below are given the figures of production (in m. tonnes) of a rice factory:

Year	2012	2013	2014	2015	2016	2017	2018
Production (in m. tonnes)	80	90	92	83	94	99	92

(i) Fit the straight line trend to these figures and calculate trend values.
(ii) Estimate the likely sales of the company during 2019.

Answer

(i) Filling straight line trend

Year (t)	Production (y)	x= t-2015	xy	$x^2$	Trend Values $\left(y_t\right)$
2012	80	-3	-240	9	84
2013	90	-2	-180	4	86
2014	92	-1	-92	1	88
2015	83	0	0	0	90
2016	94	1	94	1	92
2017	99	2	198	4	94
2018	92	3	276	9	96
n=7	$\Sigma y$=630	$\Sigma x$=0	$\Sigma$ xy=56	$\Sigma x^2=28$

Now, $a=\frac{\Sigma y}{n}=\frac{630}{7}=90$
$b=\frac{\Sigma x y}{\Sigma x^2}=\frac{56}{28}=2$
Thus, trend equation is : $y_t=90+2 x$
Trend values are
$\begin{array}{l}y_{2012}=90+2(-3)=84
\\ y_{2013}=90+2(-2)=86
\\ y_{2014}=90+2(-1)=88
\\ y_{2015}=90+2(0)=90
\\ y_{2016}=90+2(1)=92
\\ y_{2017}=90+2(2)=94
\\ y_{2018}=90+2(2)=96\end{array}$
(ii)Now,
For $2019, x$ would be 4 .
Putting $x=4$ in trend equation, we get
$y_{2019}=90+2(4)=98$

View full question & answer→

Question 25 Marks

From the following data calculate the 4- yearly moving averages and determine the trend values

Years	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021
Value	50.0	36.5	43.0	44.5	38.9	38.9	32.6	41.7	41.4	33.8

Answer

Calculation of Trend values by it four yearly Moving Averages

Year	Value	4- yearly centered Moving Total	4- yearly Moving Average (Trend values)	4- yearly centered Moving Average
2012	50.0
		-
2013	36.5
		174.0	43.5
2014	43.0			42.12
		162.9	40.73
2015	44.5			41.03
		165.3	41.33
2016	38.9			40.03
		154.9	38.73
2017	38.9			38.38
		152.1	38.03
2018	32.6			38.31
		154.3	38.58
2019	41.7			37.94
		149.2	37.3
2020	41.1
		-
2021	33.8

View full question & answer→

Question 35 Marks

Calculate four-Yearly moving averages of number of students studying in a higher secondary school in a particular city from the following data.

Year	Number of Students
2011	124
2012	120
2013	135
2014	140
2015	145
2016	158
2017	162
2018	170
2019	175

Answer

Computation of four-yearly moving averages:

Year	Sales	4-yearly centered moving total	4- yearly moving average	4- yearly centered moving Average
2011	124	-	-	-
			-
2012	120	-	-	-
		519	129.75
2013	135	-		132.37
		540	135.00
2014	140	-		139.75
		578	144.50
2015	145	-		147.87
		605	151.25
2016	158	-		155.00
		635	158.75
2017	162	-		162.52
		665	166.25
2018	170	-	-	-
			-
2019	175	-	-	-

View full question & answer→

Question 45 Marks

Calculate trend values from the following data assuming 5- yearly and 7- yearly moving average

Year	1	2	3	4	5	6	7	8
Value	110	104	98	105	109	120	115	110
Year	9	10	11	12	13	14	15	16
Value	114	122	130	127	122	118	130	140

Answer

Calculation of Trend values by moving average method:

Year	Value	Moving Total		Moving Average
Year	Value	5 Year	7 Year	5 Year	7 Year
1	110	-	-	-	-
2	104	-	-	-	-
3	98	526	-	105.2	-
4	105	536	761	107.2	108.71
5	109	547	761	109.4	108.71
6	120	559	771	111.8	110.14
7	115	568	795	113.6	113.57
8	110	581	820	116.2	117.14
9	114	591	838	118.2	119.71
10	122	603	840	120.6	120.00
11	130	615	843	123.0	120.43
12	127	619	863	123.8	123.29
13	122	627	889	125.4	127.00
14	118	637	-	127.4	-
15	130	-	-	-	-
16	140	-	-	-	-

View full question & answer→

Question 55 Marks

Fit the straight line trend to the following time series data:

Year	2017	2018	2019	2020	2021
Sale of sugar (in thousand kg)	80	90	92	83	94

Also, tabulate the trend values

Answer

Year t	Sales y	x = t-2019	xy	$x^2$	$y_t$
2017	80	-2	-160	4	83.6
2018	90	-1	-90	1	85.7
2019	92	0	0	0	87.8
2020	83	1	83	1	89.9
2021	94	2	188	4	92.0
n =5	$\Sigma y=439$	$\Sigma x=0$	$\Sigma x y=21$	$\Sigma x^2=10$

Now, $a=\frac{\Sigma y}{n}=\frac{439}{5}=87.8$
$b=\frac{\Sigma x y}{\Sigma x^2}=\frac{21}{10}=2.1$
Hence, trend equation is $y_t=87.8+2.1 x$
$
\begin{array}{l}
y_{2017}=87.8+2.1(-2)=83.6 \\
y_{2018}=87.8+2.1(-1)=85.7 \\
y_{2019}=87.8+2.1(0)=87.8 \\
y_{2000}=87.8+2.1(1)=89.9 \\
y_{2021}=87.8+2.1(2)=92.0
\end{array}
$

View full question & answer→

Applied Maths 5 Marks Questions

Test yourself on this topic