Statistics

Question 1

What is the most important principle in statistics?

Answer 1

Correlation doesn’t imply causation!

Question 2

What are the various possibilities when 2 data sets (X and Y) are correlated?

Answer 2

1) X causes Y
2) Y causes X
3) X and Y partly cause one another
4) X and Y are both caused by something else
5) Correlation is just chance, there’s no causal relationship

Question 3

What does ‘r’ represent?

Answer 3

The strength of correlation

Question 4

What are the types of correlation?

Answer 4

1) Perfect
2) Strong
3) Moderate
4) Weak
5) No correlation

Question 5

What is the difference between correlation and association?

Answer 5

Correlation: linear relationship between 2 variables (type of association)
Association: any relationship between 2 variables

Question 6

What is the r value also known as?

Answer 6

PMCC

Question 7

What does a higher r value mean? What does r=0 mean?

Answer 7

A stronger correlation. r=0 means no correlation at all

Question 8

What is interpolation? What is extrapolation?

Answer 8

Interpolation - inferences within our data (valid and reliable)
Extrapolation - inferences outside our data (unreliable)

Question 9

What should you do when drawing a line of best fit?

Answer 9

1) same number of points above and below the line
2) try to have all points equidistant from the line
3) don’t include outliers
4) don’t extend the line beyond the points (not even to the origin as you can’t infer that the trend holds!)

Question 10

What does this symbol mean: ≈?

Answer 10

Estimated value/ approximate

Question 11

What is the formula for a regression line?

Answer 11

y=a+bx

Question 12

What is a regression line?

Answer 12

A straight line showing the best fit for scattered data points on a graph, shows the linear relationship between an independent variable (X-axis) and a dependent variable (Y-axis)

Question 13

What points will a regression line always pass through?

Answer 13

The mean point, coordinate formed by the average of all x and y values in the dataset (x̄, ȳ) where the straight line represents the mean

Question 14

How do use your calculator to work out the r value of a data set?

Answer 14

1) press home and go to ‘regression’
2) type in your data down the column
3) select the subheading ‘graph’ then ‘regression’ then ‘linear’
4) select the subheading ‘stats’ and scroll down until you find the regression coeff. (r) value

Question 15

How do you plot a regression line?

Answer 15

1) Use the values of ‘a’ and ‘b’ given to you by your calculator when you work out the r value
2) Insert them into the equation: y=a+bx
3) Pick any data point in your set and insert the ‘y’ value into the equation to get x
4) Plot the (x,y) point found
5) Repeat this for several values in your data set then connect them using a straight line (this is the regression line!)

Question 16

What is standard deviation?

Answer 16

The number that tells us the average distance which the data points lie from the mean. The higher the number the larger the spread of the data.

Question 17

What are the range of possible values for ‘r’?

Answer 17

-1≤r≤1

Question 18

What does x̄ mean?

Answer 18

The mean

Question 19

What is standard deviation squared equal to?

Answer 19

The variance

Question 20

How do you find outliers?

Answer 20

Calculate x̄ + 2σx and x̄ - 2σx to get a range of data values (that includes 95% of your data), any values that fall outside these bounds are outliers

Question 21

Define systematic sampling

Answer 21

This is where every nth person or item in the population is selected (after using a method to randomly select the first person)

Question 22

What are the advantages and disadvantages of systematic sampling?

Answer 22

Advantages: can be used for quality control on a production line, should give an unbiased sample
Disadvantages: if intervals coincide with a pattern in the population then the sample could be biased

Question 23

How do you calculate the mode if there are several values repeated the same number of times? What if none of the values are repeated?

Answer 23

Several values repeated - write all of the repeated values separated by a comma
None - no mode

Question 24

How do you use your calculator to calculate standard deviation?

Answer 24

1) Home button
2) Press statistics
3) Type in your data
4) select the ‘stats’ tab and then scroll down to standard deviation

Question 25

What is the equation for calculating **sample** standard deviation?

Answer 25

sx = √ (Σ(x-x̄)^2) / n-1 The **whole term is square rooted** not just the dividend. This equation is the same as one of the standard deviation equation equations, except it has a divisor of n-1 instead of n

Question 26

What are the 2 equations for standard deviation?

Answer 26

1) **√ (Σ(x-x̄)^2) /n** where ‘x’ represents an individual data point and ‘n’ is the number of data points. The **whole term** is square rooted. 3) **√ (Σx^2)/n (-x̄^2)** All terms are under the square root and Σx^2)/n is a separate fraction which x̄^2 is subtracted from. **Σx^2 this means square each individual data point separately then add them up**

Question 27

What is the standard deviation symbol?

Answer 27

σ

Question 28

What equations do you use for boxplots to determine outliers?

Answer 28

UQ + 3/2(IQR) LQ - 3/2(IQR)

Question 29

What are some key points when analysing histograms?

Answer 29

1) area under the graph is (proportional/) equal to frequency (A=kf) 2) the y-axis shows **frequency density** 3) bar widths can be unequal 4) bars are touching (continuous data)

Question 30

How do you calculate frequency density?

Answer 30

Frequency / class width

Question 31

What different types of distributions are there? Describe their shapes

Answer 31

1) symmetrical (same shape curve either side of median) 2) positive skew (the graph has a long tail in the positive direction) 3) negative skew (the graph has a long tail in the negative direction)

Question 32

How do you find the mean of data shown in a histogram?

Answer 32

(Σ (midpoint x frequency)) / total frequency

Question 33

Can you be asked to draw cumulative frequency diagrams, boxplots or histograms?

Answer 33

No

Question 34

What is stratified sampling?

Answer 34

If a population is divided into categories a stratified sample uses the same proportions of each category in the sample as there is in the population.

Question 35

What are the advantages and disadvantages of stratified sampling?

Answer 35

Advantages: if the categories are mutually exclusive this should give a representative sample Disadvantage: extra process to decide who will be surveyed can be expensive (in terms of time or money)

Question 36

How are cumulative frequency graphs plotted?

Answer 36

Endpoint (of x-axis value) against cumulative frequency

Question 37

What is useful about cumulative frequency graphs?

Answer 37

They allow us to measure the spread of data

Question 38

When analysing boxplots what values should you compare?

Answer 38

**Range or IQR** and the **median**

Question 39

Give 5 key facts about the large data set

Answer 39

1) 5 different propulsion types: petrol, diesel, electric, gas/petrol, electric/petrol 2) 3 regions: North West, London and South West 3) 2 years of registration: 2002 & 2016 4) Types of emission produced: CO2, CO and nitrous oxides 5) 5 car manufacturers: BMW, Ford, Vauxhall, Volkswagen, Toyota

Question 40

What does combinations mean? What does permutations mean?

Answer 40

Combinations: order doesn’t matter. Permutations: order does matter.

Question 41

What is the value of 0! ?

Answer 41

1

Question 42

What does nCr mean and what numbers can n be?

Answer 42

“n choose r”. n can be zero or above (positives but not negatives! This is the same for r) **n must also be greater than or equal to r**

Question 43

What is the factorial function’s symbol and what does it mean?

Answer 43

n! It means multiply the number by every consecutive number before it until you reach the number 1

Question 44

What is 4! ?

Answer 44

4x3x2x1=24

Question 45

What is the formula for combinatorics?

Answer 45

n! / (r! (n-r)!)

Question 46

How can you write “n choose r”?

Answer 46

(n,r) where the n is above the r like in a vector Or nCr where the n is the highest and the other letters are each to the left and slightly lower

Question 47

How do you get “n choose r” up on your calculator?

Answer 47

Press tool box then probability then combinatorics then (n,r)

Question 48

In (n,2) what is the lowest number n could be?

Answer 48

2 because n≥r

Question 49

Simplify (n,2)

Answer 49

1) n! / (2!(n-2)!) 2) n(n-1)(n-2)… / 2(n-2)(n-3)… 3) cancel out the upper and lower fractions, simplifying to get 1/2n(n-1)

Question 50

What is nCr used to calculate?

Answer 50

Combinations e.g. 5c2 means how many different ways are there of choosing 2 things from 5

Question 51

What number is on the edges of Pascal’s triangle?

Answer 51

1

Question 52

What number is the first row in Pascal’s triangle? What about the first column?

Answer 52

Row/column **zero**

Question 53

What do the rows and columns in Pascal’s triangle represent?

Answer 53

Rows: how many items you’re choosing from Columns: how many options you’re choosing from the total (The answer tells you the number of possible combinations)

Question 54

How do you work out the next row of Pascal’s triangle?

Answer 54

The numbers diagonally above the one you want to work out sum to make that number

Question 55

PMCC stand for?

Answer 55

Product Moment Correlation Coefficient

Question 56

State one type of emission where more than 80% of the data is known for cars in the entire UK Department for Transport Stock Vehicle Database

Answer 56

CO2

Question 57

Rahman claims there is an error in the large data set because there is no data for the CO emissions of a Toyota from the SW. Use your knowledge of the data set to comment on his claim.

Answer 57

It’s incorrect as not all values of CO are known in the large data set

Question 58

Anna claims the mean CO2 emissions for Fords first registered in London in 2016 is 0.485 g/km. Use your knowledge of the large data set to explain why this value must be incorrect.

Answer 58

CO2 emissions are in **10s and 100s** of grams per kilometre

Question 59

Why is the large data set limited?

Answer 59

It doesn’t include all car types, there are only 2 years of registration, only 3 regions and **there isn’t data for CO emissions for all of the cars in the data set**

Question 60

Denzel wants to buy a car with a propulsion type other than petrol or diesel. He takes a sample from the LDS of the CO2 emissions (g/km) of cars with one particular propulsion type. The sample is: 82, 13, 96, 49, 96, 92, 70, 81. Using your knowledge of the LDS state which propulsion type this sample is for, giving a reason for your answer

Answer 60

Electric/petrol as this is the only category with this many values