What is a frequency in the context of mathematical tools?

A frequency is how often something occurs within a dataset. It can be expressed as a percentage or as a decimal .

What is direct proportionality ?

Direct proportionality is seen when two variables increase or decrease at the same rate as each other.

True or False? The mean is the middle number in a dataset.

False. The mean is the average of all values within a dataset. The median is the middle number in a dataset.

Define the term mode .

The mode, or modal value, is the most frequent value in a dataset.

What is standard deviation ?

Standard deviation is a measure of the spread of data around the mean value.

What is scientific notation?

Scientific notation is a way of writing very large or very small numbers , e.g. 3 500 000 = 3.5 × 10 6 .

What is Simpson's reciprocal index used for?

Simpson's reciprocal index is used to measure the relative biodiversity of a given community.

What is the purpose of the Lincoln Index ?

The Lincoln Index is used to estimate population size during capture-mark-recapture sampling.

What is the t-test used to determine?

The t-test is used to determine whether the means of two sets of data are significantly different .

In the International System of Units (SI), what is the correct unit for pressure ?

The correct unit for pressure in the SI system is the pascal (Pa) .

In the International System of Units, what is the symbol for the unit of length ?

The symbol for the SI base unit of length is m for metre.

What is the SI base unit for mass ?

The SI base unit for mass is the kilogram ( kg ).

True or False? The prefix micro represents 10 -9 .

False. The prefix micro represents 10 -6 .

What does the prefix kilo represent?

The prefix kilo represents 10 3 .

What is the SI base unit for the amount of a pure substance ?

The SI base unit for the amount of substance is the mole ( mol ).

True or False? 1 cm 3 is equivalent to 1 millilitre (ml).

True. 1 cm 3 is equivalent to 1 millilitre (ml).

What is uncertainty in measurement?

Uncertainty is the range of values around a measurement within which the true value is expected to lie .

What is meant when a length measurement has an uncertainty of ±0.05 cm .

An uncertainty of ±0.05 cm means that the true value could be up to 0.05 cm more or less than the recorded measurement.

True or False? Error and uncertainty are the same thing.

False. Error and uncertainty are not the same . error = the difference between a measured value and the true value uncertainty = the range within which the true value lies

What can error bars show?

Error bars are graphical representations of the variability of data and can indicate: uncertainty range degrees of precision standard error standard deviation

True or False? Error bars that represent standard deviation can be used to assess whether or not two data sets are significantly different to each other.

True. Error bars that represent standard deviation can be used to assess whether or not two data sets are significantly different to each other Overlapping error bars indicate that two sets of data are not significantly different .

What is the coefficient of determination (R²)?

The coefficient of determination (R²) is a measure of how well a trend line or curve on a graph fits its data set .

What does a correlation coefficient of +1 indicate?

A correlation coefficient of +1 indicates a completely positive correlation .

True or False? A correlation coefficient of 0 means there is no correlation between variables.

True. A correlation coefficient of 0 means there is no correlation between variables.

What is the purpose of a chi-squared test ?

A chi-squared test determines whether the difference between observed and expected values is significant .

True or False? The independent variable is plotted on the y-axis of a graph.

False. The independent variable is plotted on the x-axis of a graph .

What is a line of best fit ?

A line of best fit is a line drawn through data points on a graph to show the trend of the data .

True or False? A line of best fit must pass through all data points.

False. A line of best fit does not have to pass through all data points. Where the data is scattered the points should be evenly distributed on either side of the best fit line.

Define the term gradient in the context of a graph.

The gradient of a graph is a measure of the steepness of the slope of a line . It can be calculated by dividing the change in the y-axis by the change in the x-axis.

Define the term tangent in graphing.

A tangent is a straight line that touches a curve at a single point and has the same slope as the curve at that point.

Define the term maxima in reference to graphs.

Maxima are the high points on a graph , at which the gradient of a line changes from positive to negative.

What is the purpose of uncertainty bars on a graph?

Uncertainty bars show the uncertainty in a specific measurement on a graph.

What is the difference between extrapolation and interpolation ?

The difference between extrapolation and interpolation is: extrapolation = extending a line of best fit to estimate values that lie beyond the data points of a graph interpolation = using a line of best fit to estimate values that lie between data points of a graph

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Tool 3: Mathematics (DP IB Biology)

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What is a frequency in the context of mathematical tools?

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Cards in this collection (37)

What is a frequency in the context of mathematical tools?
A frequency is how often something occurs within a dataset. It can be expressed as a percentage or as a decimal.
What is direct proportionality?
Direct proportionality is seen when two variables increase or decrease at the same rate as each other.
True or False?
The mean is the middle number in a dataset.
False.
The mean is the average of all values within a dataset.
The median is the middle number in a dataset.
Define the term mode.
The mode, or modal value, is the most frequent value in a dataset.
What is standard deviation?
Standard deviation is a measure of the spread of data around the mean value.
What is scientific notation?
Scientific notation is a way of writing very large or very small numbers, e.g. 3 500 000 = 3.5 × 10⁶.
What is the formula for percentage change?
The formula for percentage change is:
percentage change = (change $\div$ initial value) × 100
What is Simpson's reciprocal index used for?
Simpson's reciprocal index is used to measure the relative biodiversity of a given community.
What is the purpose of the Lincoln Index?
The Lincoln Index is used to estimate population size during capture-mark-recapture sampling.
What is the t-test used to determine?
The t-test is used to determine whether the means of two sets of data are significantly different.
In the International System of Units (SI), what is the correct unit for pressure?
The correct unit for pressure in the SI system is the pascal (Pa).
In the International System of Units, what is the symbol for the unit of length?
The symbol for the SI base unit of length is m for metre.
What is the SI base unit for mass?
The SI base unit for mass is the kilogram (kg).
True or False?
The prefix micro represents 10^-9.
False.
The prefix micro represents 10^-6.
What does the prefix kilo represent?
The prefix kilo represents 10³.
What is the SI base unit for the amount of a pure substance?
The SI base unit for the amount of substance is the mole (mol).
True or False?
1 cm³is equivalent to 1 millilitre (ml).
True.
1 cm³is equivalent to 1 millilitre (ml).
What is uncertainty in measurement?
Uncertainty is the range of values around a measurement within which the true value is expected to lie.
What is meant when a length measurement has an uncertainty of ±0.05 cm.
An uncertainty of ±0.05 cmmeans that the true value could be up to 0.05 cm more or less than the recorded measurement.
True or False?
Error and uncertainty are the same thing.
False.
Error and uncertainty are not the same.
- error = the difference between a measured value and the true value
- uncertainty = the range within which the true value lies
What can error bars show?
Error bars are graphical representations of the variability of data and can indicate:
- uncertainty
- range
- degrees of precision
- standard error
- standard deviation
True or False?
Error bars that represent standard deviation can be used to assess whether or not two data sets are significantly different to each other.
True.
Error bars that represent standard deviation can be used to assess whether or not two data sets are significantly different to each other
Overlapping error bars indicate that two sets of data are not significantly different.
What is the coefficient of determination (R²)?
The coefficient of determination (R²) is a measure of how well a trend line or curve on a graph fits its data set.
What does a correlation coefficient of +1 indicate?
A correlation coefficient of +1 indicates a completely positive correlation.
True or False?
A correlation coefficient of 0 means there is no correlation between variables.
True.
A correlation coefficient of 0 means there is no correlation between variables.
Describe the correlation shown below.
This graph shows a strong positive correlation.
What is the purpose of a chi-squared test?
A chi-squared test determines whether the difference between observed and expected values is significant.
What type of graph is shown in the image below?
The image shows a box and whisker diagram, or box plot.
True or False?
The independent variable is plotted on the y-axis of a graph.
False.
The independent variable is plotted on the x-axis of a graph.
What is a line of best fit?
A line of best fit is a line drawn through data points on a graph to show the trend of the data.
True or False?
A line of best fit must pass through all data points.
False.
A line of best fit does not have to pass through all data points. Where the data is scattered the points should be evenly distributed on either side of the best fit line.
Define the term gradient in the context of a graph.
The gradient of a graph is a measure of the steepness of the slope of a line. It can be calculated by dividing the change in the y-axis by the change in the x-axis.
Define the term tangent in graphing.
A tangent is a straight line that touches a curve at a single point and has the same slope as the curve at that point.
Define the term maxima in reference to graphs.
Maxima are the high points on a graph, at which the gradient of a line changes from positive to negative.
What is the purpose of uncertainty bars on a graph?
Uncertainty bars show the uncertainty in a specific measurement on a graph.
What is the difference between extrapolation and interpolation?
The difference between extrapolation and interpolation is:
- extrapolation = extending a line of best fit to estimate values that lie beyond the data points of a graph
- interpolation = using a line of best fit to estimate values that lie between data points of a graph
What is the purpose of the diagram below?
The diagram is pedigree diagram which is used to represent patterns of inheritance within a family.