Let's break down the problem to calculate the average relative increase in the consumer price index (CPI) over the three months.

Step 1: Define Variables

Let the initial CPI value in January be $P_0 = 100$ (since we are dealing with percentage changes, this is a common starting point).

• January: The CPI increased by 6%. So, the CPI at the end of January is: $P_1 = P_0 \times (1 + 0.06) = 100 \times 1.06 = 106$

• February: The CPI increased by 7% relative to January. So, the CPI at the end of February is: $P_2 = P_1 \times (1 + 0.07) = 106 \times 1.07 = 113.42$

• March: The CPI decreased by 10% relative to February. So, the CPI at the end of March is: $P_3 = P_2 \times (1 - 0.10) = 113.42 \times 0.90 = 102.078$

Step 2: Calculate the Total Change Over Three Months

Now, we calculate the overall relative change from January to March:

$\text{Total change} = \frac{P_3 - P_0}{P_0} = \frac{102.078 - 100}{100} = 0.02078 = 2.078\%$

Step 3: Calculate the Average Relative Increase Per Month

To find the average relative increase per month, we take the total change over three months and divide it by 3:

$\text{Average monthly increase} = \frac{2.078\%}{3} = 0.6927\%$

Thus, the average relative increase in the consumer price index per month over the three-month period is approximately 0.693%.

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Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:

1. What would the average increase be if the changes in each month were the same percentage?
2. How does a negative percentage change affect the overall calculation of the index?
3. How would the average increase change if the index increased by 5% in March instead of decreasing by 10%?
4. What would happen to the average monthly increase if the decrease in March was larger, say 20%?
5. Can we generalize this method to calculate average monthly changes over any time period?

Tip: When calculating average changes over time, small variations in monthly percentages can significantly impact the overall trend.