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Glossary page I

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Independence (in situations that involve elements of *chance*)

The property that an *outcome* of one trial of a situation involving elements of chance or a *probability activity* has no effect or influence on an outcome of any other trial of that situation or activity.

**Curriculum achievement objectives references**

Probability: Levels 4, (5), (6), (7), (8)

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Independent events

*Events* that have no influence on each other.

Two events are independent if one of the events has no influence on the *probability* of the other event occurring.

If events **A** and **B** are independent then:

P(**A | B**) = P(**A**)

P(**B | A**) = P(**B**)

P(**A and B**) = P(**A**) P(**B**), where P(**E**) represents the probability of event **E** occurring.

For two events **A** and **B**:

If P(**A | B**)= P(**A**) then **A** and **B** are independent events.

If P(**B | A**)= P(**B**) then **A** and **B** are independent events.

If P(**A and B**) = P(**A**) P(**B**) then **A** and **B** are independent events.

**Curriculum achievement objectives reference**

Probability: Level 8

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Independent variable

A common alternative term for the *explanatory variable* in *bivariate data*.

Alternatives: *explanatory variable*, input variable, predictor variable

**Curriculum achievement objectives reference**

Statistical investigation: Level (8)

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Index number

A number showing the size of a quantity relative to its size at a chosen period, called the **base period**.

The price index for a certain ‘basket’ of shares, goods, or services aims to show how the price has changed while the quantities in the basket remain fixed. The index at the base period is a convenient number such as 100 (or 1000). An index greater than 100 (or 1000) at a later time period indicates that the basket has increased in value or price relative to that at the base period.

**Curriculum achievement objectives reference**

Statistical investigation: Level (8)

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Inference

See: *statistical inference*

**Curriculum achievement objectives references**

Statistical investigation: Levels 6, 7, 8

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Interpolation

The process of estimating the value of one *variable* based on knowing the value of the other variable, where the known value is within the range of values of that variable for the *data* on which the estimation is based.

**Curriculum achievement objectives references**

Statistical investigation: Levels 7, (8)

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Interquartile range

A *measure of spread* for a *distribution* of a *numerical variable* which is the width of an interval that contains the middle 50% (approximately) of the values in the distribution. It is calculated as the difference between the *upper quartile* and *lower quartile* of a distribution.

It is recommended that, for small *data sets*, this measure of spread is calculated by sorting the values into order or displaying them on a suitable plot and then counting values to find the *quartiles*, and to use software for large data sets.

The interquartile range is a stable measure of spread in that it is not influenced by unusually large or unusually small values. The interquartile *range* is more useful as a measure of spread than the range because of this stability. It is recommended that a graph of the distribution is used to check the appropriateness of the interquartile range as a measure of spread and to emphasise its meaning as a *feature* of the distribution.

### Example

The maximum temperatures, in degrees Celsius (°C), in Rolleston for the first 10 days in November 2008 were 18.6, 19.9, 20.6, 19.4, 17.8, 18.1, 17.8, 18.7, 19.6, 18.8

Ordered values: 17.8, 17.8, 18.1, 18.6, 18.7, 18.8, 19.4, 19.6, 19.9, 20.6

The *median* is the *mean* of the two central values, 18.7 and 18.8. Median = 18.75°C

The values in the ‘lower half’ are 17.8, 17.8, 18.1, 18.6, 18.7. Their median is 18.1. The lower quartile is 18.1°C.

The values in the ‘upper half’ are 18.8, 19.4, 19.6, 19.9, 20.6. Their median is 19.6. The upper quartile is 19.6°C.

The interquartile range is 19.6°C – 18.1°C = 1.5°C

The *data* and the interquartile range are displayed on the *dot plot* below.

If you cannot view or read this graph, select this link to
open a text version.

See: *lower quartile, measure of spread, quartiles, upper quartile*

### Curriculum achievement objectives references

Statistical investigation: Levels (5), (6), (7), (8)

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Interval estimate

A range of numbers, calculated from a *random sample* taken from the *population*, of which any number in the range is a possible value for a *population parameter*.

### Example

A 95% *confidence interval* for a *population mean* is an interval estimate.

See: *estimate*

**Curriculum achievement objectives reference**

Statistical investigation: Level 8

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Investigation

See: *statistical investigation*

**Curriculum achievement objectives references**

Statistical investigation: All levels

Statistical literacy: Levels 1, 2, 3, 4, 5

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Irregular component (for *time-series data*)

The other *variations* in time-series data that are not identified as part of the* trend component, cyclical component*, or* seasonal component*. They mostly consist of variations that don’t have a clear pattern.

Alternative: random error component

See: *time-series data*

**Curriculum achievement objectives reference**

Statistical investigation: Level (8)

Last updated October 9, 2013

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