OP Malhotra Class 11 Maths Solutions Chapter 31 Moving Average Chapter Test

 

Question 1. The following table gives the recorded monthly sales figures of a certain type of television for the 18-month period commencing 1st January 1989. Calculate the 6-monthly moving averages and display these and the original figures on the same graph using the same axes for both. Comment briefly on the purpose of moving average graphs.
Answer:

Moving average graphs help to smooth out short-term ups and downs in data. By looking at averages over time, it becomes easier to see the main pattern or "trend" in the data. This helps in forecasting future values and understanding long-term changes without getting confused by daily or weekly fluctuations. For example, a 6-month moving average shows the general direction of sales over half a year, ignoring small monthly changes.
In simple words: Moving averages help to see the big picture trend in data by smoothing out small changes. This makes it easier to predict what might happen next.

🎯 Exam Tip: When calculating moving averages, be very careful with the sums and divisions. For centered moving averages, always average two consecutive moving totals to align the average with the correct period midpoint. Remember to label your graph axes and lines clearly.

 

Question 2. The following table gives the numbers of failures of commercial industries in a country during the years 1975 to 1990 . Draw a graph illustrating the figures. Calculate the 4-yearly moving average and plot them on the same graph.
Answer:

This table shows the calculation of the 4-yearly moving average for industrial failures. The graph displays both the actual number of failures each year and the smoothed trend line based on the 4-yearly moving averages. Observing the trend helps us understand the general direction of industry failures over time, making it easier to see if the situation is improving or worsening without being misled by yearly ups and downs.
In simple words: The chart and graph show how many businesses failed each year, and how that number generally changed over time by using a 4-year average to make the trend clearer.

🎯 Exam Tip: When dealing with even-numbered moving averages (like 4-yearly), remember to "center" the average by taking a 2-period average of the moving totals. This ensures the average aligns with an actual time point on the graph.

 

Question 3. The average number, in lakhs, of working days lost in strikes during each year of the period 1981-90 was
Answer:

This table shows the calculation of the 3-yearly moving average for working days lost due to strikes. The graph shows the actual number of days lost and the smoothed trend line, making it easier to see how strike activity changed over the decade. Moving averages are useful for identifying patterns or cycles that might be hidden by quick, sharp changes in the raw data.
In simple words: The table and graph show how many working days were lost each year because of strikes, and a smooth line shows the general pattern over time.

🎯 Exam Tip: For odd-numbered moving averages (like 3-yearly), the average directly aligns with the middle year of the period. Be careful with decimal places and rounding when calculating averages.

 

Question 4. The profit of a soft drink firm (in thousands of rupees) during each month of the year is as given below : Calculate the 4-monthly moving averages and plot these and the original data on a graph sheet.
Answer:

This table shows the step-by-step calculation for the 4-monthly moving averages of the soft drink firm's profit. The accompanying graph illustrates both the actual monthly profit and the smoothed trend line, which helps in identifying seasonal patterns or overall growth/decline. Using moving averages helps the company understand its sales performance better by focusing on the underlying trend rather than just monthly variations.
In simple words: The table calculates the average profit over four months, and the graph shows the real profit each month next to a smooth line that tells us the general profit pattern.

🎯 Exam Tip: When graphing monthly or quarterly data, remember to label your X-axis clearly with the time periods. For 4-monthly moving averages, you often need a centered average to place the data point accurately on the graph between months.

 

Question 5. The quarterly profits of a small scale industry (in thousands of rupees) is as follows : Calculate 4-quarterly moving averages. Display these and the original figures graphically on the same graph sheet.
Answer:

This table shows the calculation of 4-quarterly moving averages for a small industry's profits. The graph visually represents the actual quarterly profit data alongside the smoothed moving average trend. This helps to remove seasonal variations (like higher sales in certain quarters) and highlight the long-term changes in profit, making it easier to see overall business growth or decline.
In simple words: The chart and graph show how much profit the industry made each quarter and a smooth line to show its general profit trend, removing seasonal ups and downs.

🎯 Exam Tip: When dealing with quarterly data, always ensure your moving averages correctly account for the four quarters to capture a full year's cycle. Centered moving averages are key for plotting these even-period averages accurately.

 

Question 6. The number of accidents due to rash driving over a period of 3 years, is given in the following table : Calculate four quarterly moving averages and illustrate them and original figures on one graph using the same axes for both.
Answer:

This table shows the calculation of 4-quarterly moving averages for accident figures related to rash driving. The graph displays both the actual number of accidents and the smoothed trend line, making it easier to see if accident rates are generally increasing or decreasing over the years. This method helps to identify underlying patterns, which can be useful for planning safety measures.
In simple words: The chart and graph show how many accidents happened each quarter and a smooth line to show the general trend of accidents over time, helping to see if things are getting better or worse.

🎯 Exam Tip: When analyzing time series data like this, remember that a moving average helps remove short-term fluctuations, allowing you to clearly see the long-term trend. Pay attention to peaks and troughs in the actual data and how the trend line smooths them out.