Applied maths

Population

the whole set of items that are of interest

Census

observes or measures every member of a population

Sample

a selection of observations taken from a subset of the population which is used to find out information about the population as a whole

Sampling units

individual units of a population

Sampling frame

a list of sampling units of a population individually named or numbered

Simple random sample

every sample has an equal chance of being selected

Systematic sampling

the required elements are chosen at regular intervals from an ordered list

Stratified sampling

the population is divided into mutually exclusive strata and a random sample is taken from each

Quota sampling

an interviewer or researcher selects a sample that reflects the characteristics of the whole population

Opportunity sampling

consists of taking the sample from people who are available at the time the study is carried out and who fit the criteria you are looking for

Quantitative variables/ quantitative data

variables or data associated with numerical observations

Qualitative variables/ qualitative data

variables or data associated with non-numerical observations

Continuous variable

a variable that can take any value in a given range

Discrete variable

a variable that can take only specific values in a given range

Class

a group presented in a grouped frequency table

What do class boundaries tell you?

the minimum and maximum values that belong in each class

What does the midpoint of a class tell you?

the average of the class boundaries

What does the class width tell you?

the difference between the upper and lower class boundaries

Mode or modal class

the value or class that occurs most often

Median

the middle value when the data values are put in order

What is the formula for the mean?

mean = ∑x /n

What is the formula for the mean for data in a frequency table?

mean = ∑xƒ/∑ƒ

Range

the difference between the largest and smallest values in the data set

How do you find the lower quartile for discrete data?

n ÷ 4, if it is a whole number the lower quartile is halfway between this data point and the one above, if it is not round up and pick that data point

How do you find the upper quartile for discrete data?

n x ¾, if it is a whole number the upper quartile is halfway between this data point and the one above, if it is not round up and pick that data point

Interquartile range

the difference between the upper quartile and lower quartile

Interpercentile range

the difference between the values for two given percentiles

What is the formula for variance in a frequency table?

σ²=∑ƒx²/∑ƒ - (∑ƒx/∑ƒ)²

What is the formula for standard deviation for grouped data?

σ=√(∑ƒx²/∑ƒ - (∑ƒx/∑ƒ)²)

If data is coded for using y=x-a/b, what is the mean of the coded data?

mean= mean of x - a / b

If data is coded for using y=x-a/b, what is the standard deviation of the coded data?

σ_y= σ_x / b

Cleaning the data

the process of removing anomalies from a data set

What is the equation for the frequency density of a bar of a histogram?

frequency density= frequency/class width

What should you comment on when comparing data sets?

a measure of location, a measure of spread

What is a frequency polygon?

when each bar in a histogram with equal class widths in a histogram is joined in the middle

Bivariate data

data which has pairs of values for two variables

Correlation

the nature of the linear relationship between two variables

What do you use the regression line to do?

make predictions for values of the dependent variable that are within the range of the given data

What is the regression line of y on x?

y=a +bx

If the equation of a regression line is y=a +bx and b is positive what does it tell you?

the data is positively correlated

If the equation of a regression line is y=a +bx and b is negative what does it tell you?

the data is negatively correlated

What is a venn diagram used for?

to represent events graphically, frequencies or probabilities can be placed in regions of the venn diagram

What is the formula for mutually exclusive events?

P(A or B) = P(A) + P(B)

What can a tree diagram be used for?

to show the outcomes of two or more events happening in succession

What does a Probability distribution do?

it fully describes the probability of any outcome in a sample space

What are the conditions to model X with a binomial distribution (n,p)?

there are a fixed number of trials, there are two possible outcomes, there is a fixed probability of success, the trials are independent of each other

Null hypothesis

the hypothesis you assume to be correct

What does the Alternative hypothesis tell you?

the parameter if your assumption is wrong

Critical region

a region of the probability distribution which if the test statistic falls within it, would cause you to reject the null hypothesis

Critical value

the first value to fall within the critical region

The actual significance level of a hypothesis test

the probability of incorrectly rejecting the null hypothesis

What are hypothesis tests with an alternative hypothesis in the form H₁:p<… and H₁:p>… are called?

one tailed tests

What are hypothesis tests with an alternative hypothesis in the form H₁:p≠…. are called?

two tailed tests

What happens to the critical region in a two tailed test?

It is split at either end of the distribution

What is the SI unit for mass?

Kg

What is the SI unit for length or displacement?

m

What is the SI unit for time?

s

Vector

a quantity with both magnitude and direction

Scalar

a quantity with only magnitude

What is distance the magnitude of?

displacement

What is speed the magnitude of?

velocity

What does the gradient on a displacement-time graph represent?

velocity

What is velocity?

the rate of change of displacement

What is the equation for average velocity?

displacement from starting point/ time taken

What is the equation for average speed?

total distance traveled/time taken

What is acceleration?

the rate of change of velocity

What does the gradient of a velocity-time graph represent?

acceleration

What does the area between the velocity-time graph and the x-axis represent?

distance traveled

What do you need to know about objects under gravity?

it causes all objects to accelerate towards earth, if the effects of air resistance are ignored the acceleration is constant, it does not depend on the mass of the object

What is the value of g?

9.8ms⁻¹

Newton’s first law of motion

an object at rest will stay at rest and that an object moving with constant velocity will continue to move with constant velocity unless an unbalanced force acts on the object

Newton’s second law of motion

F=ma

What is the equation for weight?

mass x gravity

Newton’s third law of motion

every action has an equal and opposite reaction

If displacement is expressed as a function of t what is the velocity?

v= ds/dt

If velocity is expressed as a function of t what is the acceleration?

a = dv/dt

How do you calculate the moment of F about a point?

|F| x d(perpendicular distance)

Resultant moment

the sum of moments acting on a body

When a rigid body is in equilibrium what is the resultant force and resultant moment?

0N, 0Nm

If a rigid body is on the point of tilting about a pivot what does it mean?

the reaction at any other support is 0

What is the component of a force of magnitude F in a certain direction?

FCosθ where θ is the size of the angle between the force and the direction

To solve problems involving inclined planes it is easier to…..

resolve parallel to and at right angles to the plane

What is the equation for the maximum or limiting value of the friction between two surfaces?

Fr=µ x R

What is the horizontal motion of a projectile modeled as?

having a constant velocity

What is the vertical motion of a projectile modeled as?

having constant acceleration due to gravity (a=9.8ms⁻¹)

When the velocity of the vertical direction of a projectile is 0 what does it mean?

it has reached its greatest hight

What does it mean if a particle or rigid body is in static equilibrium?

it is at rest and the resultant force acting upon it is 0

If a body is said to be in limiting equilibrium what does it mean?

The maximum value of the frictional force is reached when the body is on the point of moving

In general the force of friction is……

F≤µ x R

What is the resultant moment of a rigid body in static equilibrium?

0