Business Statistics Quiz: Index Numbers And Percent Change
20 questions · exam conditions
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Index Numbers And Percent ChangeQuestion 1 of 20

An employee's nominal salary was $80,000 in 2021 and rose to $85,000 in 2023. Over the same period, the Consumer Price Index (CPI) increased from 125.0 to 135.0. By what approximate percentage did the employee's real salary change from 2021 to 2023?

An increase of 6.25%
An increase of 8.00%
A decrease of 1.60%
A decrease of 1.75%
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Business Statistics Quiz

Business Statistics Quiz: Index Numbers And Percent Change

Practice Index Numbers And Percent Change in Business Statistics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Index Numbers And Percent Change, giving you a quick way to practice the rules, question types, and explanations that matter most for Business Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

An employee's nominal salary was $80,000 in 2021 and rose to $85,000 in 2023. Over the same period, the Consumer Price Index (CPI) increased from 125.0 to 135.0. By what approximate percentage did the employee's real salary change from 2021 to 2023?

  1. An increase of 6.25%
  2. An increase of 8.00%
  3. A decrease of 1.60% (correct answer)
  4. A decrease of 1.75%
Explanation: This is a multi-step problem. First, calculate the real salary for both years using the formula: Real Salary = (Nominal Salary / CPI) * 100.
  1. Real Salary 2021 = ($80,000 / 125.0) * 100 = $64,000.
  2. Real Salary 2023 = ($85,000 / 135.0) * 100 ≈ $62,962.96.
  3. Then, calculate the percentage change in real salary: (\frac{62,962.96−62,962.96 - 64,000}{$64,000} \times 100 \approx -1.62%). This is an approximate decrease of 1.60%.
Distractor Reasoning: (A) is the percentage change in nominal salary, ignoring the effect of inflation. (B) is the percentage change in the CPI (inflation rate), not the change in real salary. (D) results from a slight miscalculation, possibly by rounding intermediate steps differently or using a slightly incorrect formula.

Question 2

A price index for a basket of goods increased from 108.5 to 125.3 over a three-year period. If the index is rebased so that the final year becomes the new base year (index = 100), what would be the index value for the initial year in the rebased system?

  1. 79.8
  2. 86.6 (correct answer)
  3. 115.5
  4. 120.2
Explanation: When rebasing with the final year as base (125.3 → 100), the initial year becomes: (108.5/125.3) × 100 = 86.6. Choice A incorrectly calculates (108.5/136.5) × 100. Choice C uses (125.3/108.5) × 100. Choice D uses an incorrect rebasing formula.

Question 3

An aggregate price index uses three commodities with the following weights: Commodity A (40%), Commodity B (35%), Commodity C (25%). If the individual price relatives are 112, 108, and 95 respectively, what is the weighted aggregate price index?

  1. 105.0
  2. 106.4 (correct answer)
  3. 108.3
  4. 110.2
Explanation: Weighted index = (0.40 × 112) + (0.35 × 108) + (0.25 × 95) = 44.8 + 37.8 + 23.75 = 106.35 ≈ 106.4. Choice A uses simple average (112+108+95)/3 = 105. Choice C weights incorrectly. Choice D uses weights as whole numbers instead of decimals.

Question 4

A company wants to adjust its 2019 revenue of $2.4 million to 2023 dollars using a price deflator that was 110.5 in 2019 and 126.8 in 2023. What is the inflation-adjusted revenue, and what does this represent?

  1. $2.75 million; shows what 2023 revenue would be in 2019 purchasing power
  2. $2.09 million; shows what 2019 revenue equals in 2023 purchasing power
  3. $2.75 million; shows what 2019 revenue equals in 2023 purchasing power (correct answer)
  4. $2.09 million; shows what 2023 revenue would be in 2019 purchasing power
Explanation: When you encounter price deflator problems, you're dealing with inflation adjustment—converting monetary values from one time period to another to account for changes in purchasing power. The key is understanding what the deflator represents and which direction you're converting. To adjust 2019 revenue to 2023 dollars, you multiply by the ratio of deflators: Adjusted Value=Original Value×Target Year DeflatorBase Year Deflator\text{Adjusted Value} = \text{Original Value} \times \frac{\text{Target Year Deflator}}{\text{Base Year Deflator}} Here: $2.4 million×126.8110.5=$2.4×1.147=$2.75 million\$2.4 \text{ million} \times \frac{126.8}{110.5} = \$2.4 \times 1.147 = \$2.75 \text{ million} This shows what the 2019 revenue equals in 2023 purchasing power—essentially asking "if that $2.4 million from 2019 were earned today, what would it be worth?" Answer A gives the correct calculation but misinterprets the meaning. It describes converting 2023 revenue to 2019 purchasing power, which is the opposite of what we're doing. Answer B makes the calculation error of using the inverse ratio (110.5/126.8 = 0.871), giving $2.09 million, and also misinterprets the direction. Answer D combines both errors—wrong calculation and wrong interpretation of what the adjustment represents. Remember this pattern: when adjusting historical values to current dollars, you multiply by (current deflator/historical deflator), and the result shows what the old money equals in today's purchasing power. The deflator ratio greater than 1 indicates inflation occurred, so the nominal value increases.

Question 5

A production index shows the following quarterly values: Q1=98.5, Q2=102.3, Q3=106.8, Q4=103.2. What is the percent change from the lowest to highest quarter, and which calculation method gives the most meaningful comparison for management?

  1. 8.4% increase; compare each quarter to base period index of 100
  2. 4.5% increase; compare each quarter to annual average index
  3. 6.8% increase; compare each quarter to previous quarter sequentially
  4. 8.4% increase; compare highest quarter directly to lowest quarter (correct answer)
Explanation: When analyzing index data, you need to identify what comparison will provide the most actionable insights for decision-makers. Index values represent relative performance, and the choice of comparison method depends on what management needs to understand. To find the percent change from lowest to highest quarter, first identify the extremes: Q1 has the lowest value (98.5) and Q3 has the highest (106.8). The percent change calculation is: 106.8−98.598.5×100=8.4%\frac{106.8 - 98.5}{98.5} \times 100 = 8.4\% This direct comparison between the highest and lowest quarters gives management the clearest picture of the production range's volatility and peak performance relative to the weakest period. Option A calculates the correct percentage but suggests comparing to a base index of 100, which doesn't capture the actual range within this data set. Option B incorrectly calculates 4.5% and proposes using an annual average, which would smooth out the meaningful quarterly variations that management needs to see. Option C suggests 6.8% with sequential quarter comparisons, but this percentage is wrong and sequential analysis wouldn't capture the full range from minimum to maximum performance. The most meaningful comparison for management is the direct highest-to-lowest calculation because it immediately shows the production system's range of performance variability, helping managers understand both the potential upside and the gap they need to address from their worst-performing period. Study tip: When working with index data, always consider what comparison gives stakeholders the most actionable insight—often it's the direct comparison between extremes rather than complex averaging methods.

Question 6

A regional economic index increased by 4.2% in Year 1, decreased by 2.8% in Year 2, and increased by 6.1% in Year 3. If the index started at 100, what is the average annual percent change over the three-year period, and what is the index value at the end of Year 3?

  1. Average = 2.5%; Final index = 107.7
  2. Average = 2.5%; Final index = 107.5
  3. Average = 2.4%; Final index = 107.7 (correct answer)
  4. Average = 2.4%; Final index = 107.5
Explanation: When you encounter percentage changes over multiple periods, you're dealing with compound growth calculations. The key insight is that percentage changes multiply rather than add, and you need to find the geometric mean to get the true average annual change. To find the final index value, multiply the starting value by each year's growth factor. Year 1: 100×1.042=104.2100 \times 1.042 = 104.2. Year 2: 104.2×0.972=101.28104.2 \times 0.972 = 101.28 (since a 2.8% decrease means multiplying by 0.972). Year 3: 101.28×1.061=107.46101.28 \times 1.061 = 107.46, which rounds to 107.5. For the average annual percent change, use the geometric mean formula: 1.042×0.972×1.0613−1\sqrt[3]{1.042 \times 0.972 \times 1.061} - 1. This equals 1.07443−1=1.0244−1=0.0244\sqrt[3]{1.0744} - 1 = 1.0244 - 1 = 0.0244 or 2.4%. Answer A is wrong because it uses 2.5% for the average, which would result from incorrectly using the arithmetic mean (4.2%−2.8%+6.1%)/3=2.5%(4.2\% - 2.8\% + 6.1\%)/3 = 2.5\%. Answer B makes the same arithmetic mean error and also miscalculates the final index as 107.7 instead of 107.5. Answer D correctly calculates the 2.4% geometric mean but incorrectly shows the final index as 107.7. Remember: with sequential percentage changes, always use the geometric mean for the average rate, and multiply growth factors (not percentages) to find cumulative effects. The arithmetic mean of percentages gives misleading results in compound scenarios.

Question 7

A company's quarterly sales are tracked using a sales index, with Q1 2020 as the base period (Index = 100). The index value for Q3 2022 was 145.5, and for Q3 2023, it was 152.775. What was the percentage increase in sales from Q3 2022 to Q3 2023?

  1. 5.0% (correct answer)
  2. 7.275%
  3. 4.76%
  4. 52.775%
Explanation: The percentage change between two periods using index numbers is calculated as New Index−Old IndexOld Index×100\frac{\text{New Index} - \text{Old Index}}{\text{Old Index}} \times 100. Here, the calculation is 152.775−145.5145.5×100=7.275145.5×100=5.0%\frac{152.775 - 145.5}{145.5} \times 100 = \frac{7.275}{145.5} \times 100 = 5.0\%. Distractor Reasoning: (B) is incorrect because it is the simple subtraction of the two index values (152.775 - 145.5), which represents the change in points, not the percentage change. (C) is incorrect because it uses the new index value (152.775) as the denominator, a common error in percent change calculations. (D) is incorrect as it represents the percentage change from the base period to Q3 2023 (152.775 - 100), not the change from Q3 2022 to Q3 2023.

Question 8

In January 2024, the Consumer Price Index (CPI) for a country was 180.0, using 2010 as the base year (Index = 100). If a representative basket of goods and services cost $900 in January 2024, what would have been the approximate cost of the same basket in 2010?

  1. $1,620
  2. $500 (correct answer)
  3. $720
  4. $1,125
Explanation: The formula relating prices and an index is: Index = Current CostBase Period Cost×100\frac{\text{Current Cost}}{\text{Base Period Cost}} \times 100. To find the base period cost, we rearrange the formula: Base Period Cost = Current CostIndex×100\frac{\text{Current Cost}}{\text{Index}} \times 100. Plugging in the values: Base Period Cost = (\frac{900}{180.0} \times 100 = 5 \times 100 = $500). Distractor Reasoning: (A) results from incorrectly multiplying the current cost by the index as a decimal ($900 ×\times 1.80 = $1,620). (C) results from subtracting the index value from the cost ($900 - 180 = $720), which is a nonsensical operation. (D) results from dividing the current cost by the percentage increase (900 / 0.80), a misunderstanding of how the index works.

Question 9

Over a five-year period, a company's nominal revenue doubled. During the same period, the relevant industry price index increased from 120 to 160. What was the approximate percentage change in the company's real revenue over this period?

  1. An increase of 100%
  2. An increase of 67%
  3. An increase of 50% (correct answer)
  4. An increase of 33%
Explanation: Let's assign values to track the change. Let nominal revenue at the start be $100. Since it doubled, nominal revenue at the end is $200.
  1. Calculate the starting real revenue. Real revenue is proportional to Nominal RevenuePrice Index\frac{\text{Nominal Revenue}}{\text{Price Index}}. So, Real Revenue (start) ∝100120≈0.833\propto \frac{100}{120} \approx 0.833.
  2. Calculate the ending real revenue. Real Revenue (end) ∝200160=1.25\propto \frac{200}{160} = 1.25.
  3. Calculate the percentage change between these two real revenue values: 1.25−0.8330.833×100=0.4170.833×100≈50%\frac{1.25 - 0.833}{0.833} \times 100 = \frac{0.417}{0.833} \times 100 \approx 50\%.
Distractor Reasoning: (A) is the change in nominal revenue, not real revenue. (B) is the result of incorrectly subtracting the inflation rate from the nominal growth rate: 100%−(160−120120)%=100%−33.3%=66.7%100\% - (\frac{160-120}{120})\% = 100\% - 33.3\% = 66.7\%. (D) is the percentage increase in the price index (inflation) over the period.

Question 10

The price of a commodity increases by 10% in Year 1, and then decreases by 10% in Year 2. What is the net percentage change in the price from the beginning of Year 1 to the end of Year 2?

  1. 0% change
  2. A 1% decrease (correct answer)
  3. A 1% increase
  4. A 2% decrease
Explanation: Let the original price be P. After a 10% increase in Year 1, the price becomes P×(1+0.10)=1.10PP \times (1 + 0.10) = 1.10P. In Year 2, this new price decreases by 10%. The new price is 1.10P×(1−0.10)=1.10P×0.90=0.99P1.10P \times (1 - 0.10) = 1.10P \times 0.90 = 0.99P. The final price is 99% of the original price, which represents a 1% decrease. Distractor Reasoning: (A) is the most common error, resulting from incorrectly adding the percentages (+10% - 10% = 0%). This fails to account for the fact that the 10% decrease is calculated on a larger base amount. (C) would result from a sign error in the calculation. (D) is a plausible-looking incorrect answer without a direct calculation path.

Question 11

A market-capitalization-weighted stock index includes Stock A (market cap $500 billion) and Stock B (market cap $50 billion). One day, Stock A's price increases by 1%, and Stock B's price increases by 10%. Assuming all other stocks in the index remain unchanged, which statement best describes the effect of these price changes on the index?

  1. The price increase of Stock A will have a greater impact on the index.
  2. The price increase of Stock B will have a greater impact on the index.
  3. The price changes in Stock A and Stock B will have an equal impact on the index. (correct answer)
  4. The impact cannot be determined without knowing the total market cap of the index.
Explanation: A market-capitalization-weighted index moves based on the total dollar change in the market capitalization of its components. Let's calculate the dollar impact of each stock's change. Change in Stock A's market cap = (500 billion×1%=+500 \text{ billion} \times 1\% = +5 \text{ billion}). Change in Stock B's market cap = (50 billion×10%=+50 \text{ billion} \times 10\% = +5 \text{ billion}). Since both stocks add the exact same amount ($5 billion) to the total market capitalization of the index, their impact on the index value for that day is equal. Distractor Reasoning: (A) is a common misconception, focusing only on Stock A's larger weight without considering its smaller percentage change. (B) is another misconception, focusing only on Stock B's larger percentage change without considering its smaller weight. (D) is incorrect because the relative impact of these two changes on each other can be determined without knowing the total size of the index.

Question 12

A company's IT budget was $2.0 million in 2020. The budget increased by 5% in 2021 and by another 5% in 2022. An IT cost index was 110 in 2020 and 122 in 2022. What was the company's real IT budget in 2022, expressed in 2020 constant dollars?

  1. Approximately $2.21 million
  2. Approximately $1.99 million (correct answer)
  3. Approximately $1.81 million
  4. Approximately $2.00 million
Explanation: First, calculate the nominal IT budget in 2022. A 5% increase followed by another 5% increase is a total increase of 1.05×1.05=1.10251.05 \times 1.05 = 1.1025. Nominal Budget 2022 = (2.0M×1.1025=2.0M \times 1.1025 = 2.205M). Second, to convert this to 2020 constant dollars, we must deflate it by the inflation between 2020 and 2022. The inflation factor is the ratio of the indices: Index 2022Index 2020=122110\frac{\text{Index 2022}}{\text{Index 2020}} = \frac{122}{110}. Real Budget 2022 (in 2020 dollars) = (\frac{\text{Nominal Budget 2022}}{\text{Inflation Factor}} = \frac{2.205M}{122/110} = 2.205M \times \frac{110}{122} \approx $1.988M). This is approximately $1.99 million. Distractor Reasoning: (A) is the nominal budget for 2022, ignoring inflation. (C) is the real budget expressed in the index's base-year dollars ((2.205M/1.22≈2.205M/1.22 \approx 1.81M)), not in 2020 constant dollars. (D) is a guess that the nominal increase and inflation cancelled each other out.

Question 13

In January, a region's unemployment rate was 5.0%. In February, it rose to 6.0%. During the same period, a price index rose from 250 to 260. Which statement correctly compares the relative (percentage) changes of these two metrics?

  1. The relative increase in the price index was greater than the relative increase in the unemployment rate.
  2. A valid relative comparison is not possible because the metrics use different units (percent vs. points).
  3. The two metrics had the same relative increase of 10%.
  4. The relative increase in the unemployment rate was greater than the relative increase in the price index. (correct answer)
Explanation: When comparing changes in different metrics, you need to calculate the relative (percentage) change for each one separately. Relative change shows proportional growth regardless of the original units or scale. For the unemployment rate: it changed from 5.0% to 6.0%. The relative change is 6.0−5.05.0×100%=1.05.0×100%=20%\frac{6.0 - 5.0}{5.0} \times 100\% = \frac{1.0}{5.0} \times 100\% = 20\% For the price index: it changed from 250 to 260. The relative change is 260−250250×100%=10250×100%=4%\frac{260 - 250}{250} \times 100\% = \frac{10}{250} \times 100\% = 4\% The unemployment rate increased by 20% while the price index increased by only 4%. Therefore, answer D is correct—the relative increase in unemployment rate was greater. Answer A is backwards—it incorrectly states the price index had the greater relative increase. Answer B reflects a common misconception that different units prevent comparison, but relative changes are unitless percentages that allow valid comparisons. Answer C makes the classic error of focusing on absolute changes (both went up by simple arithmetic differences) rather than calculating true percentage changes relative to their starting values. Remember this key principle: when comparing changes across different metrics, always calculate relative changes using the formula new value−old valueold value×100%\frac{\text{new value} - \text{old value}}{\text{old value}} \times 100\%. Don't be fooled by absolute differences—a 1-point change means very different things when starting from 5 versus starting from 250.

Question 14

A price index for a basket of goods is 115 in Year 3 and 125 in Year 4. The base year is Year 1. A student makes two claims:

I. The price of the basket increased by 10 percentage points from Year 3 to Year 4.

II. The price of the basket increased by approximately 8.7% from Year 3 to Year 4. Which of the student's claims is/are correct?

  1. I only
  2. Neither I nor II
  3. Both I and II
  4. II only (correct answer)
Explanation: When you encounter price index questions, remember that these numbers represent relative price levels compared to a base year, and there's a crucial difference between percentage point changes and percentage changes. Let's evaluate each claim using the given data: Year 3 index = 115, Year 4 index = 125. For Claim I: The difference between the indices is 125 - 115 = 10. This represents a 10 percentage point increase, which is correct. When we say "percentage points," we're simply subtracting the raw index values. For Claim II: To find the actual percentage change, you calculate: 125−115115×100%=10115×100%=8.7%\frac{125 - 115}{115} \times 100\% = \frac{10}{115} \times 100\% = 8.7\%. This claim is also correct. Since both claims are mathematically sound, the answer is C) Both I and II. Wait - let me recalculate to verify: 10115=0.087=8.7%\frac{10}{115} = 0.087 = 8.7\%. Both claims are indeed correct. Looking at the wrong answers: A) I only ignores that the percentage calculation in Claim II is also valid. B) Neither I nor II incorrectly rejects both mathematically correct statements. D) II only wrongly dismisses the valid percentage point calculation in Claim I. The key study tip: Always distinguish between percentage point changes (simple subtraction of index values) and percentage changes (which require dividing by the starting value). Both are valid ways to express change, but they yield different numbers and have different interpretations.

Question 15

A company uses a simple average of price relatives to construct a price index for two key components, A and B. In the base year, both components were priced at $100. In the current year, component A is priced at $150 and component B is priced at $90. What is the value of the index for the current year?

  1. 120.0 (correct answer)
  2. 116.7
  3. 125.0
  4. 100.0
Explanation: When you encounter price index questions, you're dealing with a fundamental tool for measuring how prices change over time. A simple average of price relatives method requires you to calculate each component's price relative (current price ÷ base price × 100), then average those relatives. Let's work through this step-by-step. For component A: the price relative is 12080×100=150\frac{120}{80} \times 100 = 150. For component B: the price relative is 120120×100=100\frac{120}{120} \times 100 = 100. Using the simple average method, you add these relatives and divide by the number of components: 150+1002=2502=125\frac{150 + 100}{2} = \frac{250}{2} = 125. This confirms answer D) 125.0 is correct. Now let's see why the other options are wrong. Answer A) 120.0 might tempt you because both current prices are $120, but this ignores the index calculation method entirely. Answer B) 100.0 would be correct only if prices hadn't changed at all, which isn't the case here since component A increased significantly. Answer C) 112.5 appears to be a calculation error – perhaps someone incorrectly weighted the components or made an arithmetic mistake. Remember that price indices using simple averages of price relatives give equal weight to each component regardless of their absolute price levels or economic importance. This means a 50% increase in component A (from $80 to $120) has the same impact as no change in component B, resulting in an overall index above 100 even though one component's price remained constant.

Question 16

A stock price index starts at 100 in January, increases by 15% to February, then decreases by 12% from February to March. What is the index value in March, and what is the overall percent change from January to March?

  1. Index = 101.2; Overall change = +1.2% (correct answer)
  2. Index = 103.0; Overall change = +3.0%
  3. Index = 97.0; Overall change = -3.0%
  4. Index = 98.8; Overall change = -1.2%
Explanation: January to February: 100 × 1.15 = 115. February to March: 115 × 0.88 = 101.2. Overall change: (101.2-100)/100 = +1.2%. Choice B incorrectly adds/subtracts percentages (15%-12%=3%). Choice C uses 100-15%+12%. Choice D makes a calculation error in the final multiplication.

Question 17

A company uses a simple average of price relatives to construct a price index for two key components, A and B. In the base year, component A was priced at $80 and component B was priced at $120. In the current year, both components are priced at $120. What is the value of the index for the current year?

  1. 120.0
  2. 100.0
  3. 112.5
  4. 125.0 (correct answer)
Explanation: When you encounter price index questions, you're dealing with a fundamental tool for measuring how prices change over time. A simple average of price relatives method requires you to calculate each component's price relative (current price ÷ base price × 100), then average those relatives. Let's work through this step-by-step. For component A: the price relative is 12080×100=150\frac{120}{80} \times 100 = 150. For component B: the price relative is 120120×100=100\frac{120}{120} \times 100 = 100. Using the simple average method, you add these relatives and divide by the number of components: 150+1002=2502=125\frac{150 + 100}{2} = \frac{250}{2} = 125. This confirms answer D) 125.0 is correct. Now let's see why the other options are wrong. Answer A) 120.0 might tempt you because both current prices are $120, but this ignores the index calculation method entirely. Answer B) 100.0 would be correct only if prices hadn't changed at all, which isn't the case here since component A increased significantly. Answer C) 112.5 appears to be a calculation error – perhaps someone incorrectly weighted the components or made an arithmetic mistake. Remember that price indices using simple averages of price relatives give equal weight to each component regardless of their absolute price levels or economic importance. This means a 50% increase in component A (from $80 to $120) has the same impact as no change in component B, resulting in an overall index above 100 even though one component's price remained constant.

Question 18

A company's sales index (base year 2018) was 110 in 2021. In 2022, the company's nominal sales increased by 15%, but the sales index only increased to 112. What is the most likely explanation for this discrepancy?

  1. The base year for the index was changed between 2021 and 2022.
  2. The index is a price index, not a quantity index, and prices fell significantly.
  3. The index measures real sales, and there was significant inflation during 2022. (correct answer)
  4. The index is unweighted, while the sales increase was concentrated in low-volume products.
Explanation: A sales index can track nominal or real sales. A 15% increase in nominal sales should lead to a large increase in a nominal sales index. The index only increased from 110 to 112, a change of 112−110110≈1.8%\frac{112-110}{110} \approx 1.8\%. This small increase, despite a large nominal sales jump, suggests the index is tracking real (inflation-adjusted) sales. The 15% nominal increase was largely offset by high inflation, resulting in only a small increase in the volume of goods sold. Distractor Reasoning: (A) Changing the base year would rescale the numbers but wouldn't explain why a 15% increase corresponds to such a small index change. (B) A sales index tracks revenue, which is Price × Quantity. If prices fell significantly, a 15% increase in revenue would imply a very large increase in quantity, which should be reflected in a real sales index. This explanation is unlikely. (D) Weighting could cause discrepancies, but it is less likely to explain such a large gap between nominal growth (15%) and real growth (1.8%) than high inflation.

Question 19

A price index series for a commodity has a base year of 2015 (Index = 100). The index value for 2018 was 120, and the index value for 2020 was 150. If the base year is shifted from 2015 to 2018, what will be the new index number for 2020?

  1. 125.0 (correct answer)
  2. 130.0
  3. 80.0
  4. 30.0
Explanation: To re-base an index series, you divide every value in the old series by the old index value of the new base year, and then multiply by 100. The new base year is 2018, and its old index value was 120. New Index for 2020 = Old Index for 2020Old Index for 2018×100=150120×100=1.25×100=125.0\frac{\text{Old Index for 2020}}{\text{Old Index for 2018}} \times 100 = \frac{150}{120} \times 100 = 1.25 \times 100 = 125.0. Distractor Reasoning: (B) is an incorrect adjustment, potentially from adding the difference in index points (150 + (100-120) = 130). (C) is incorrect because it inverts the ratio in the calculation (120 / 150 * 100 = 80). (D) is incorrect because it is the simple difference between the two old index values (150 - 120 = 30).

Question 20

A government agency maintained a price index with a base year of 1990. This series was discontinued at the end of 2010, at which point its value was 250. A new, revised index was started with a base year of 2010 (Index = 100). The new index had a value of 110 in 2015. To create a continuous series, the new index is spliced to the old one. What is the resulting index value for 2015 on the original 1990 base?

  1. 44.0
  2. 260.0
  3. 275.0 (correct answer)
  4. 360.0
Explanation: To splice the new series onto the old one, we need a conversion factor. At the overlap year (2010), the old index was 250 and the new index was 100. The factor to convert new values to the old scale is Old Index at OverlapNew Index at Overlap=250100=2.5\frac{\text{Old Index at Overlap}}{\text{New Index at Overlap}} = \frac{250}{100} = 2.5. To find the 2015 value on the old (1990) scale, multiply the 2015 new index value by this factor: Spliced Index for 2015 = 110×2.5=275.0110 \times 2.5 = 275.0. Distractor Reasoning: (A) results from inverting the splicing factor (110 * (100/250)). (B) results from incorrectly adding the difference between the indices at the overlap year (110 + (250-100) = 260) or by adding the 10 point change in the new index to the old index value (250+10=260). (D) is an arbitrary large number resulting from a significant calculation error, possibly 250+110=360.