PART 1 : TIME SERIES - Gujarat Board (GSEB) STD 12 Commerce Statistics Questions

Q 1MCQ1 Mark

Which method of determining trend fails to give trend estimates for some period in the beginning as well as in the end ?

A
Graphical method
B
Least square method
✓
Moving average method
D
Karl Pearson's method

Answer: C.

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Q 2MCQ1 Mark

The data about census survey in India conducted every ten years from independence till $2011$ are shown in a time series. What will be the value of $\bar{t}$ for these data?

A
$2.5$
✓
$4$
C
$3$
D
$3.5$

Answer: B.

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Q 3MCQ1 Mark

If $\bar{y}=38$ and $b=3.2$ are found from a time series of five months, what should be the value of $a$ ?

A
$47.6$
✓
$28.4$
C
$46$
D
$30$

Answer: B.

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Q 4MCQ1 Mark

If the linear equation obtained from the data of six years for a variable is $\hat{y}=-20.5-4 t$, what will be the estimate of the value for the seventh year?

A
$48.5$
✓
$-48.5$
C
$8.5$
D
$-8.5$

Answer: B.

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Q 5MCQ1 Mark

State the notation used for the disturbance variable of the linear model of a time series.

A
$\Delta_t$
B
$e_t$
✓
$u_t$
D
$\hat{e}_t$

Answer: C.

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Q 61 Marks Each1 Mark

Which method is useful to determine trend by removing the effect of short term variations.

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Q 71 Marks Each1 Mark

State the methods used to find trend in time series.

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Q 81 Marks Each1 Mark

Which component is obtained when the effect of trend and regular component is removed from the variable $y_f$ of a time series?

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Q 91 Marks Each1 Mark

Write two illustrations of irregular or random component.

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Q 101 Marks Each1 Mark

State the factors responsible for variations due to random component.

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Q 112 Marks Each2 Marks

If $n=8, b=3.05$ and $a=23.56$ for a time series, find the estimated value of variable $y$ for $t=9$.

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Q 122 Marks Each2 Marks

If $n=6, \bar{y}=55.33$ and $b=-0.06$, find the linear equation for trend.

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Q 132 Marks Each2 Marks

If $\bar{t}=3, \Sigma y=615$ and $\Sigma t y=1910$ for a time series, find the linear equation for trend.

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Q 142 Marks Each2 Marks

The linear equation for the trend of a time series is $\hat{y}=71.78-5.08 t$. State the values of $a$ and $b$. Also find the trend values for $t=6$ and $t=7$.

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Q 152 Marks Each2 Marks

The trend line for a time series of the production of sugar $($in quintals$)$ is $\hat{y}=55.9+6.7 t$. Find the trend value for $t=3$ and $t=5$.

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Q 163 Marks Each3 Marks

If $\bar{t}=3.5, \Sigma y=36, \Sigma t y=134$ for a time series, find the linear equation.

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Q 173 Marks Each3 Marks

The following data is available for the variable $y$ of a time series. Fit a linear equation from it.
$n=9, \Sigma y=214, \Sigma t y=1051$

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Q 183 Marks Each3 Marks

Fit a linear equation from the following data about the variable $y$ of a time series.
$n=6, \Sigma y=378, \Sigma t y=1399$

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Q 193 Marks Each3 Marks

The information about the sale $($in lakh $₹)$ of a general store during the first ten months of the year $2019$ is as follows. Obtain the trend of this time series using the graphical method.

Time $t ($month$)$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
Sale $y_{(t)} ($lakh $₹)$	$12$	$24$	$20$	$15$	$19$	$22$	$25$	$41$	$44$	$38$

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Q 203 Marks Each3 Marks

The following data are obtained about the female-male ratio from the census surveys in India for seven decades after independence. Obtain the linear trend by graphical method.

Year	$1951$	$1961$	$1971$	$1981$	$1991$	$2001$	$2011$
Female-Male ratio	$946$	$941$	$930$	$934$	$927$	$933$	$943$

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Q 214 Marks Each4 Marks

The information about wholesale price index numbers $(WPI)$ announced by the central government is as follows. Find the trend from it using four monthly moving averages.

Month	Apr$-18$	May	June	July	August	Sept.	Oct.	Nov.	Dec.	Jan.-	Feb.	March
$WPI$	$3.62$	$4.78$	$5.69$	$5.27$	$4.53$	$5.13$	$5.28$	$4.64$	$3.46$	$2.76$	$2.93$	$3.18$

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Q 224 Marks Each4 Marks

The details of quarterly production of sugar in a factory are as follows. Find the trend in the series from it using moving averages of four quarters.

Year	$2016$				$2017$				$2018$
Quarter	$Q_{(1)}$	$Q_{(2)}$	$Q_{(3)}$	$Q_{(4)}$	$Q_{(1)}$	$Q_{(2)}$	$Q_{(3)}$	$Q_{(4)}$	$Q_{(1)}$	$Q_{(2)}$	$Q_{(3)}$	$Q_{(4)}$
Production of sugar $($quintal$)$	$50$	$54$	$60$	$62$	$64$	$72$	$75$	$78$	$80$	$83$	$88$	$90$

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Q 234 Marks Each4 Marks

Find the trend using four monthly moving averages from the following information about the monthly profits $($in crore $₹)$ of a multinational company.

Month	Jan.	Feb.	March	April	May	June	July	Aug.	Sept.	Oct.	Nov.	Dec.
Profit $($crores$)$	$11$	$12$	$15$	$18$	$20$	$22$	$25$	$26$	$28$	$29$	$30$	$32$

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Q 244 Marks Each4 Marks

The data about $GDP-$growth rate announced by the central government is as follows. Find the trend from it using four yearly moving averages.

Year	$2006$	$2007$	$2008$	$2009$	$2010$	$2011$	$2012$	$2013$	$2014$	$2015$	$2016$	$2017$
$GDP$ growth rate $($percent$)$	$9.3$	$9.8$	$3.9$	$8.5$	$10.3$	$6.9$	$5.5$	$6.4$	$7.4$	$8.2$	$7.1$	$6.6$

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Q 254 Marks Each4 Marks

The cost of living index number in a city is given in the following table. Obtain trend from it using five yearly moving averages.

Year	$2009$	$2010$	$2011$	$2012$	$2013$	$2014$	$2015$	$2016$	$2017$	$2018$
Cost of living index number	$176$	$180$	$184$	$190$	$203$	$230$	$275$	$264$	$280$	$288$

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Q 265 Mark Each5 Marks

The information about wholesale price index numbers $(WPI)$ announced by the central government is as follows. Find the trend from it using four monthly moving averages.

Month	Apr-18	May	June	July	August	Sept.	Oct.	Nov.	Dec.	Jan.-	Feb.	March
$WPI$	$3.62$	$4.78$	$5.69$	$5.27$	$4.53$	$5.13$	$5.28$	$4.64$	$3.46$	$2.76$	$2.93$	$3.18$

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Q 275 Mark Each5 Marks

The details of quarterly production of sugar in a factory are as follows. Find the trend in the series from it using moving averages of four quarters.

Year	$2016$				$2017$				$2018$
Quarter	$Q_{(1)}$	$Q_{(2)}$	$Q_{(3)}$	$Q_{(4)}$	$Q_{(1)}$	$Q_{(2)}$	$Q_{(3)}$	$Q_{(4)}$	$Q_{(1)}$	$Q_{(2)}$	$Q_{(3)}$	$Q_{(4)}$
Production of sugar $($quintal$)$	$50$	$54$	$60$	$62$	$64$	$72$	$75$	$78$	$80$	$83$	$88$	$90$

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Q 285 Mark Each5 Marks

Find the trend using four monthly moving averages from the following information about the monthly profits $($in crore $₹)$ of a multinational company.

Month	Jan.	Feb.	March	April	May	June	July	Aug.	Sept.	Oct.	Nov.	Dec.
Profit $($crores$)$	$11$	$12$	$15$	$18$	$20$	$22$	$25$	$26$	$28$	$29$	$30$	$32$

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Q 295 Mark Each5 Marks

The data about $GDP-$growth rate announced by the central government is as follows. Find the trend from it using four yearly moving averages.

Year	$2006$	$2007$	$2008$	$2009$	$2010$	$2011$	$2012$	$2013$	$2014$	$2015$	$2016$	$2017$
$GDP$ growth rate $($percent$)$	$9.3$	$9.8$	$3.9$	$8.5$	$10.3$	$6.9$	$5.5$	$6.4$	$7.4$	$8.2$	$7.1$	$6.6$

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Q 305 Mark Each5 Marks

The cost of living index number in a city is given in the following table. Obtain trend from it using five yearly moving averages.

Year	$2009$	$2010$	$2011$	$2012$	$2013$	$2014$	$2015$	$2016$	$2017$	$2018$
Cost of living index number	$176$	$180$	$184$	$190$	$203$	$230$	$275$	$264$	$280$	$288$

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PART 1 : TIME SERIES question types

PART 1 : TIME SERIES questions

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PART 1 : TIME SERIES Statistics - PART 1 : TIME SERIES

PART 1 : TIME SERIES question types

PART 1 : TIME SERIES questions

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