Index Numbers & Moving Averages Quiz - ICSE Class 11 Mathematics

Free practice quiz: Index Numbers & Moving Averages (ICSE Class 11 Mathematics). 10 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

Sample questions

1. If Laspeyres' Index for 2023 is 130 and Paasche's Index for 2023 is 125 (base year 2022), what is the approximate value of Marshal-Edgeworth Index?

   1. 127.5
   2. 127.4
   3. 127.6
   4. 128.0
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   Answer: A. 127.5

   The Marshall-Edgeworth Index is the simple arithmetic mean of Laspeyres' and Paasche's Indices. ME = (L + P) / 2. ME = (130 + 125) / 2 = 255 / 2 = 127.5.

2. A 3-period moving average is used to smooth a time series. If the first moving average value is calculated for the 3rd observation, the second for the 4th, and so on, what is the relationship between the number of data points (N) and the number of moving averages (MA_N) for a moving average of length 'k'?

   1. MA_N = N - k
   2. MA_N = N - k + 1
   3. MA_N = N
   4. MA_N = N - (k-1)
   Show answer

   Answer: B. MA_N = N - k + 1

   To calculate the first moving average of length 'k', you need 'k' data points. To calculate the last moving average, you need the last 'k' data points. Therefore, you lose (k-1) data points from the original series. If you have N data points, the number of moving averages that can be calculated is N - (k-1) = N - k + 1. For example, with N=10 and k=3, you lose 2 points, so you get 10-2 = 8 moving averages, which is 10 - 3 + 1 = 8.

3. A 5-year moving average is applied to a time series. How many fewer smoothed values will be generated compared to the original number of data points?

   1. 3
   2. 4
   3. 5
   4. 6
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   Answer: B. 4

   For a moving average of length 'k', you lose (k-1) data points. With k=5, you lose (5-1) = 4 data points. Therefore, there will be 4 fewer smoothed values than the original number of data points.

4. A trend is being analyzed using a 3-year moving average. The values are: 70, 75, 72, 78, 76, 80. What is the trend value for the 4th year?

   1. 72.33
   2. 75.00
   3. 76.00
   4. 77.00
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   Answer: B. 75.00

   The trend value for the 4th year using a 3-year moving average is the average of the data from the 2nd, 3rd, and 4th years. Trend_4 = (Value_2 + Value_3 + Value_4) / 3 = (75 + 72 + 78) / 3 = 225 / 3 = 75.00.

5. Which type of moving average is most appropriate for removing seasonality when the seasonal period is even (e.g., quarterly data)?

   1. Simple Moving Average
   2. Centered Moving Average
   3. 2 x 2 Moving Average
   4. Moving Average of Moving Averages
   Show answer

   Answer: C. 2 x 2 Moving Average

   When the seasonal period 'n' is even, a simple moving average of length 'n' will not be centered on an actual data point. A '2 x 2 moving average' (or a moving average of moving averages where the initial averages are taken over n/2 periods) is used to center the moving average for even periods, allowing for better trend isolation.

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