Higher Applications of Maths

correlation coefficient

measures the strength of a linear relationship

correlation coefficient = 0.843

strong positive correlation

correlation coefficient = - 0.364

weak negative correlation

the p-value is < 0.05

we can reject the null hypothesis, there is a significant difference between the two means.

why can't we make future predictions based on only a few pieces of data?

Sample size is too small to make assumptions, we are extrapolating too far if we assume a trend continues well into the future

how do you calculate the rate of change?

m = change in y/change in x or m = V/H

which type of mathematical relationship is this:

Weight = 1.05 (Height) + 30

Linear relationship (y=mx+c)

which type of mathematical relationship is this:

Loan = 3000 x 1.03^years

Exponential relationship (y = Cb^x)

which type of mathematical relationship is this:

Un = 0.65 (Un-1) + 30

Recurrence relationship

what comments can you make about boxplots

1) If there are any outliers present

2) Which group has the larger spread

3) Which group has the higher median

What type of data is: The height of a plant

numerical continuous

What type of data is: A person's heart rate

numerical continuous

What type of data is: A person's method of transport

categorical nominal

What type of data is: The number of pupils in a school

numerical discrete

what is the r-studio code for: computing the correlation coefficient

cor.test (X,Y)

what is the r-studio code for: computing the coefficient of determination (r-squared)

summary(lm(Y~X))

what does the coefficient of determination (r-squared) measure?

how much of the variation in the data can be explained by our model. A high r-squared value is good.

what is the r-studio code for: getting the coefficients needed to write your regression equation

lm(Y~X) Remember Y is the dependent variable

Name 2 measures of location

mean and median

Name 2 measures of spread

standard deviation and IQR

What measures of location and spread would you use for normally distributed data

mean and standard deviation

what measures of location and spread would you use for data with a skewed distribution

median and IQR

What is the Excel function for: calculating the mean

=AVERAGE(...

What is the Excel function for: calculating the total

=SUM(...

What is the Excel function for: keeping cell G7 constant

G$7

What is the Excel function for: calculating the standard deviation

=STDEV(...

In PERT charts what is the critical path

the shortest time the entire project can be completed in (which is the longest path on the chart)

How do you calculate the area of a rectangle

A = length x breadth

How do you calculate the area of a triangle

A = 1/2 x base x height

which hypothesis test would you use: to determine if there is a significant difference between the mean of 2 different groups

two sample t-test (since two seperate groups)

which hypothesis test would you use: to determine if there is a significant difference between the mean exam score before and after revision

paired t-test (since based on the same person twice)

which hypothesis test would you use: to determine if there is a significant difference in the proportion of one group to the proportion of another

z-test