The following table shows gross capital information (in Crore ₹) for years 1966 to 1975: | Years | 1966 | 1967 | 1968 | 1969 | 1970 | | --- | --- | --- | --- | --- | --- | | Gross Capital information | 20 | 25 | 25 | 30 | 35 | | Years | 1971 | 1972 | 1973 | 1974 | 1975 | | Gross Capital information | 30 | 45 | 40 | 55 | 65 | Obtain trend values using 5-yearly moving values.

The following table shows gross capital informatio – Class 12 Mathematics And Statistics

Question 15 of 25

The following table shows gross capital information (in Crore ₹) for years 1966 to 1975:

Years	1966	1967	1968	1969	1970
Gross Capital information	20	25	25	30	35
Years	1971	1972	1973	1974	1975
Gross Capital information	30	45	40	55	65
Obtain trend values using 5-yearly moving values.

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2023Subjective· 3mImportance★★★★★

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Take 5-year moving totals of the data, divide each by $5$ , and centre on the middle year: the trend values are $27, 29, 33, 36, 41, 47$ for $1968$ – $1973$ .

Data (Gross Capital, Crore ₹): $1966{=}20$ , $1967{=}25$ , $1968{=}25$ , $1969{=}30$ , $1970{=}35$ , $1971{=}30$ , $1972{=}45$ , $1973{=}40$ , $1974{=}55$ , $1975{=}65$ .

5-yearly moving totals and averages (average is centred at the 3rd year of each block):

$1966$ – $1970$ : $20+25+25+30+35 = 135 \Rightarrow \dfrac{135}{5} = 27$ (centred at $1968$ )
$1967$ – $1971$ : $25+25+30+35+30 = 145 \Rightarrow \dfrac{145}{5} = 29$ (at $1969$ )
$1968$ – $1972$ : $25+30+35+30+45 = 165 \Rightarrow \dfrac{165}{5} = 33$ (at $1970$ )
$1969$ – $1973$ : $30+35+30+45+40 = 180 \Rightarrow \dfrac{180}{5} = 36$ (at $1971$ ) …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set ANNUAL1 mark
$Q. The following table shows the production of pig-iron and ferroalloys ('000 metric tons) Years 197419751976197719781979198019811982 Production 0499854810 Find trend values for the above data by using 5 yearly moving averages.$
›Reveal solutionSolution
5-year moving totals $=30,35,35,34,35$ ; dividing by 5 gives trend values $6, 7, 7, 6.8, 7$ centred on 1976–1980.

Data (production in '000 metric tons):

Year 1974 1975 1976 1977 1978 1979 1980 1981 1982
Production 0 4 9 9 8 5 4 8 10

A 5-yearly moving average is found by summing five consecutive values and dividing by 5, and the result is written against the middle (3rd) year of that group.

5-year moving totals and averages:

$1974\text{–}1978$ : $0+4+9+9+8 = 30 \Rightarrow 30/5 = 6$ (centred 1976)

$1975\text{–}1979$ : $4+9+9+8+5 = 35 \Rightarrow 35/5 = 7$ (centred 1977)

$1976\text{–}1980$ : $9+9+8+5+4 = 35 \Rightarrow 35/5 = 7$ (centred 1978)

$1977\text{–}1981$ : $9+8+5+4+8 = 34 \Rightarrow 34/5 = 6.8$ (centred 1979) …
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CBSE 2025Set ANNUAL1 markMCQ
$Q. Moving averages are useful in identifying ______.$
(a) Seasonal component
(b) Irregular component
(c) Trend component
(d) Cyclical component
›Reveal solutionSolution

A moving average averages successive groups of values, cancelling short-term ups and downs and revealing the smooth long-term direction of the series — the trend component.

A time series has four components: trend, seasonal, cyclical and irregular. The method of moving averages computes the average of a fixed number of consecutive observations and slides this window along the series. Averaging tends to cancel the seasonal, cyclical and irregular fluctuations (which oscillate above and below the general level), leaving behind the …

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Years	1974	1975	1976	1977	1978	1979	1980	1981	1982
Production	0	4	9	9	8	5	4	8	10
Find trend values for the above data by using 5 yearly moving averages.

Year	1974	1975	1976	1977	1978	1979	1980	1981	1982
Production	0	4	9	9	8	5	4	8	10

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