The weighted relatives (family budget) method computes the cost of living index as the weighted average of the price relatives, $\text{CLI} = \dfrac{\sum IW}{\sum W}$, so the given formula is correct.

In the weighted relative method (also called the family budget method) for the cost of living index number:

• For each item or group, the price relative is $I = \dfrac{p_1}{p_0}\times 100$, comparing the current price $p_1$ with the base price $p_0$.
• Each relative is assigned a weight $W$, usually the expenditure (value) of that item, $W = p_0 q_0$.

The cost of living index is then the weighted mean of these relatives:

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Purchasing power of money $=\dfrac{1}{\text{Cost of living index number}}\times 100$, so the cost-of-living index is indeed used to calculate the purchasing power of money; the statement is True.

The cost-of-living index number (consumer price index) measures the average change in the prices of a fixed basket of goods and services consumed by a particular group of people. When prices rise, the same amount of money buys less, so the purchasing power of money falls. This inverse relationship is expressed as …

By the weighted relative (family budget) method, the cost-of-living index number is $\text{CLI}=\dfrac{\sum I\,W}{\sum W}$, where $I=\dfrac{p_1}{p_0}\times 100$ is each commodity's price relative and $W$ is its weight.

The weighted relative method builds the cost-of-living index from the price relatives of the individual commodities:

• For each commodity, compute the price relative $I=\dfrac{p_1}{p_0}\times 100$, comparing the current price $p_1$ with the base price $p_0$.
• Assign each commodity a weight $W$ (usually its base-year value $W=p_0 q_0$, reflecting its share in the family budget).
• Take the weighted arithmetic mean of the price relatives: …