1st year exam prep

Question 1

Quantitative data: Meaning, Types and Examples

Answer 1

Number or quantity of data.

Discrete: Counts of things (occurrences, amounts of qualitative data)

Continuous: Numerical scale measured over time (number of degrees, seconds, meters)

Question 2

Qualitative data, Meaning, Types and Examples

Answer 2

Standard is just Data giving information on something. Verbal or narrative data. It can also be;

Nominal: Numerical coding (reference number)

Ordinal: Giving a ranking or order to something (Best to worst)

Question 3

Define: Mean, Mode, Median, Range, Standard Deviation

Answer 3

Average, Most common, Middle, Max-Min, spread of data

Question 4

Explain Histograms

Answer 4

Graph of “bins”(class boundaries) against frequency of data falling into that bin. Bar chart can be expressed as line. Skewed = non symmetrical. Tail = lines from peak

“Long tail right” Indicates that mean is above median

Question 5

Equation for standard deviation:

Answer 5

s = SQRT((sum(x-mean)^2)/(n-1))

A larger S means more unrealiable data / worse quality

Question 6

Explain Quartiles

Answer 6

Median = middle value
25th percentile = middle of bottom and median
75th percentile = middle of top and median
IQR = 75th - 25th

Points may be in-between numbers if even numbers left and right

Question 7

Method of least squares

Answer 7

Equations are given - solve them simultaneously

r^2 = 1 - ∑(y.-(fx.)) / ∑(y.-Ymean)

r^2 = 1- (SUM e / SUM(y-ymean)

The closer r^2 is to 1, the better the fit.

So if SUM e = 0 then its a perfect fit!

Question 8

Matrices need to know:

Answer 8

Multiplying rules (add when multiplying)

(R1xC1)(R2xC2) C1 and R2 need to match. And will make a (R1xC2) matrix

Representing in matrix form be careful with negatives

Transposes flip the matrix

Question 9

Polynomial roots

Answer 9

Highest power equals number of roots (real or imaginary)

Question 10

Bisection method

Answer 10

Xr = Xlower + Xupper / 2
Use side which has a sign change and repeat with new uppers and lowers

Error value = Xr new - Xr old / Xr new

Question 11

Newton-Raphson method

Answer 11

Xnew = X - F(x)/F’(x)

Error value = Xr new - Xr old / Xr new

Question 12

Z-score

Answer 12

Z= (x - xaverage) / s

Determines how many sd’s the x value is from the mean

Question 13

What is Categorical data?

Answer 13

Both nominal and ordinal data. So a numerical coding giving rank to something. (10=great 1=terrible etc.)

Question 14

What is Interval Data?

Answer 14

Quantitative and Qualitative. So a count of Qualitative data. (how many cars are red, blue, black etc)
Counted in bin values (for the example it would be different colours)
displayed using histogram.

Question 15

What are Garbage values?

Answer 15

Bits of data that don’t fit with others but can be explained

Question 16

What are “Black sheep”?

Answer 16

Bits of data that dont match the rest and cant be explained:

Question 17

What is eye-balling raw data? What to do with it?

Answer 17

Searching the raw data for trends and errors.
When finding errors:

Check, explain and correct

Accommodate, Incorporate, reject.

Question 18

What are Pareto charts?

Answer 18

Vertical bar chart with a line plot showing running total.

Column data descending.

Question 19

Explain the theory of standard deviations

Answer 19

One standard deviation covers approximately 2/3 of the total data.
Two standard deviations cover approximately 95% of the total data.
A higher SD shows that the data is more spread.

Question 20

Tally Charts

Answer 20

Chart of three lines or boxes:
Grouped ranges (bin values)
frequency or occurrences. using a tally mark notation
Then a total box

Question 21

Dot plots

Answer 21

Graphs where:
x = a value of some sort
y=dots to signify frequency of value

Question 22

Stem and leaf

Answer 22

way of displaying raw frequency in order.

Raw numbers visable and gives frequency visualisation

Question 23

scatter graph

Answer 23

graph relating two quantities x and y with a dot to show data.
Used to find a correlation.

Question 24

Inverse of 2x2 matrix:

Answer 24

Inverse = adj/det

where adj = d -b
-c a

and det = (ad-bc)

Question 25

Inverse of 3x3 matrix?

Answer 25

PROBS WONT NEED but…

Inverse = adj/det

where adj = Matrix of minors x (+ - +) etc then transposed

and det = normal det of 3x3: ( a(det1) - b(det2) + c(det3) )

Question 26

How to find roots using quadratic equation:

Answer 26

First rearrange to a form like x^2 + x + c (ie dont have the x^2 to be negative)

use x= (-b +/- SQRT(b^2 -4ac))/2a