Statistics & Applications

Trends & Data

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applied

The first m-year moving average of the data 10, 20, 30, 40, 50 is 30. The value of m is

✅ Correct Option: 4

A moving average groups consecutive numbers, adds them, and divides by the count. The "m-year moving average" groups $m$ consecutive numbers. The "first" moving average starts from the beginning of the data.

Given data: 10, 20, 30, 40, 50

First m-year moving average = 30

For $m = 2$ :

First moving average $= \dfrac{10 + 20}{2}$

$= \dfrac{30}{2}$

$= 15$

For $m = 3$ :

First moving average $= \dfrac{10 + 20 + 30}{3}$

$= \dfrac{60}{3}$

$= 20$

For $m = 4$ :

First moving average $= \dfrac{10 + 20 + 30 + 40}{4}$

$= \dfrac{100}{4}$

$= 25$

For $m = 5$ :

First moving average $= \dfrac{10 + 20 + 30 + 40 + 50}{5}$

$= \dfrac{150}{5}$

$= 30$

The value $m = 5$ gives the first moving average of 30.

2026: 19 May Shift 2

For the given five values 10, a, 13, b, 25, the 3-years moving averages are 15, 18, 19. The value of a+b is

2025: 16 May Shift 1

The following data shows the percentage of rural and urban Indian households who have a high speed internet connection.

Year (x)	Rural Household (y%)	Urban Household (y%)
2020	2	6
2021	3	7
2022	3	9
2023	4	15
2024	5	20

Based on the above data, which of the following statements are correct?

(A) A straight line trend by the method of the least squares for rural Indians is $y^t$ = 3.4 + 0.7 (x - 2022)

(B) A straight line trend by the method of the least squares for urban Indians is $y^t$ = 11.4 + 4.3 (x - 2022)

(D) The forecast for the year 2025 for rural group using the trend equation is 5.5 %.

Choose the correct answer from the options given below:

2025: 3 June Shift 2

Which of the following statements are TRUE?

(A) The sales of woolen clothes, gold, silver etc. exhibit seasonal trends.

(B) The price of stocks in the share market repeats after a definite time interval.

(D) The rise in prices before festivals is an example of a irregular trend.

Choose the correct answer from the options given below:

2026: 18 May Shift 2

For the five values 12, $a$ , 17, 21, 22, the three years moving averages are 13, 16, 20. The value of $a$ is

2025: 13 May Shift 2

For the given five values 15,24,18,33,42, the three years moving averages are

2026: 21 May Shift 1

Time series helps to

(A) derive conclusions after arranging the time series in a systematic manner.

(B) predict the future behavior of a variable.

(D) plan future operations.

Choose the correct answer from the options given below:

The first m-year moving average of the data 10, 20, 30, 40, 50 is 30. The value of m is

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