What is the index number for the base year itself, and why?

It is always 100 , because the base year's price is being compared with itself. An index number above 100 then means a price rise since the base year, and one below 100 means a fall.

What is the difference between the RPI and the CPI?

Both track the changing prices of everyday goods and services, but the CPI leaves out mortgage payments while the RPI includes them. The government uses the RPI to set student loan interest, and the CPI to set benefits and the state pension.

True or False? Gross domestic product is a type of index number.

False. GDP is the total value of all the goods and services a country produces in a period, measured in money rather than against a base year. If it falls for two or more quarters in a row, the economy is said to be in recession.

What makes a weighted index number different from an ordinary one?

It tracks several items at once, with each item given a weight reflecting how important it is. The weighted mean price then takes the place of the single price, so the index compares this year's weighted mean with the base year's.

What does a chain base index number compare a price with?

The price in the previous year, or the previous month or quarter, rather than a fixed base year. Each period is measured against the one immediately before it, so there is no single base year at all.

What does a crude birth rate actually tell you?

The number of births per 1000 people in the population. The same idea works for deaths, marriages or unemployment, by putting that count in place of the number of births.

Why can a crude death rate be misleading when comparing two towns?

Because it takes no account of the age structure of the two populations. A town with many older residents will have a high death rate simply because older people die more often, not because it is an unhealthy place to live.

Define standard population .

A notional population of exactly 1000 people, divided between the age groups in the same proportions as some real population. It is what that real population would look like shrunk down to 1000, so the figures for all its age groups add up to 1000.

How do you get the standardised rate for a whole population?

Add together the standardised rates worked out for all of its age groups. That sum is a weighted average, and it tells you what the rate would be if this population had the same age breakdown as the standard population.

True or False? A standardised rate lets you compare two populations with different age structures fairly.

True. Standardising rescales both populations to the same age breakdown, so what is left is a genuine comparison of like with like.

GCSEStatisticsEdexcelHigherFlashcardsProcessing, Representing & Analysing DataIndex Numbers & Rates of Change

Index Numbers & Rates of Change (Edexcel GCSE Statistics: Higher): Flashcards

Exam code: 1ST0

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FrontIndex Numbers
Complete the formula for an index number.
$index number = \frac{current price of item}{______} \times______$

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Cards in this collection (20)

Complete the formula for an index number.
$index number = \frac{current price of item}{______} \times______$
The completed formula is:
$index number = \frac{current price of item}{price in base year} \times 100$
What is the index number for the base year itself, and why?
It is always 100, because the base year's price is being compared with itself.
An index number above 100 then means a price rise since the base year, and one below 100 means a fall.
A pint of milk cost 36p in the base year and costs 66p now. What is the index number?
Divide the current price by the base year price and multiply by 100, giving $\frac{66}{36} \times 100 = 183.3$ to one decimal place.
No percentage sign is used with an index number, even though the calculation itself is a percentage one.
The index number for widgets in 2022 is 112.3, with 2020 as the base year. What is the percentage change since 2020?
Subtract 100 from the index number, giving $112.3 - 100 = 12.3$ as the answer.
So prices rose by 12.3% between 2020 and 2022, and a negative result would have meant a fall instead.
A thingummy cost £56.50 in the base year, and the index number is now 107.2. What does it cost now?
Divide the index number by 100 to get the multiplier 1.072, then multiply the base year price by it.
That gives $56.50 \times 1.072 = 60.568$ pounds, which rounds to £60.57 as money.
What is the difference between the RPI and the CPI?
Both track the changing prices of everyday goods and services, but the CPI leaves out mortgage payments while the RPI includes them.
The government uses the RPI to set student loan interest, and the CPI to set benefits and the state pension.
True or False?
Gross domestic product is a type of index number.
False.
GDP is the total value of all the goods and services a country produces in a period, measured in money rather than against a base year.
If it falls for two or more quarters in a row, the economy is said to be in recession.
What makes a weighted index number different from an ordinary one?
It tracks several items at once, with each item given a weight reflecting how important it is.
The weighted mean price then takes the place of the single price, so the index compares this year's weighted mean with the base year's.
The weighted mean price of Roger's pizzas was £16.25 in 2019 and £18.88 in 2023. What is the 2023 weighted index number, taking 2019 as base?
Divide the current weighted mean by the base year weighted mean and multiply by 100.
$\frac{18.88}{16.25} \times 100 = 116.2$
What does a chain base index number compare a price with?
The price in the previous year, or the previous month or quarter, rather than a fixed base year.
Each period is measured against the one immediately before it, so there is no single base year at all.
Gold cost £42.61 per gram in April 2020 and £44.17 in May. What is the chain base index number for April to May?
Divide the May price by the April price and multiply by 100, giving $\frac{44.17}{42.61} \times 100 = 103.7$ to one decimal place.
April acts as the base month here, so the price rose by 3.7 per cent over that month.
What does a crude birth rate actually tell you?
The number of births per 1000 people in the population.
The same idea works for deaths, marriages or unemployment, by putting that count in place of the number of births.
A town of 75 992 people had 783 deaths last year. What is the crude death rate?
Multiply the number of deaths by 1000 and divide by the total population.
$\frac{783 \times 1000}{75992} = 10.304$
A town of 75 992 people has a crude birth rate of 11.317. How many births were there?
Substitute into the crude rate formula and rearrange to make the number of births the subject.
$\frac{11.317 \times 75992}{1000} = 860$
The answer is rounded to a whole number, since there cannot be a fraction of a birth.
Why can a crude death rate be misleading when comparing two towns?
Because it takes no account of the age structure of the two populations.
A town with many older residents will have a high death rate simply because older people die more often, not because it is an unhealthy place to live.
Define standard population.
A notional population of exactly 1000 people, divided between the age groups in the same proportions as some real population.
It is what that real population would look like shrunk down to 1000, so the figures for all its age groups add up to 1000.
An age group holds 15 462 000 people out of a total population of 68 349 000. What is its standard population?
Divide the number in the age group by the total population and multiply by 1000.
$\frac{15462000}{68349000} \times 1000 = 226.2$
An age group has a crude death rate of 8.378 and a standard population of 385.0. What is its standardised rate?
Divide the crude rate by 1000 and multiply by the standard population.
$\frac{8.378}{1000} \times 385.0 = 3.226$
How do you get the standardised rate for a whole population?
Add together the standardised rates worked out for all of its age groups.
That sum is a weighted average, and it tells you what the rate would be if this population had the same age breakdown as the standard population.
True or False?
A standardised rate lets you compare two populations with different age structures fairly.
True.
Standardising rescales both populations to the same age breakdown, so what is left is a genuine comparison of like with like.

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