Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Excel a Level Math’s – Statistics questions and answers for 2024 candidates, Exams of Mathematics

Brunel University LondonMathematics

Excel a Level Math’s – Statistics questions and answers for 2024 candidates

Typology: Exams

2023/2024

Available from 06/07/2024

healthpro
healthpro 🇺🇸

3.8

(4)

2.4K documents

1 / 28

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Excel a Level Math’s – Statistics questions
and answers for 2024 candidates
1. Linear Regression - Correct Answers y = axⁿ
2. logy = loge + log
3. Exponential Regression - Correct Answers y = ax
4. logy = loge + log
5. Normal Approximation - Correct Answers µ = np
6. σ =√(np(1-p))
7. Mean - Correct Answers ∑x ÷ n
8. GF: ∑of ÷ ∑f
9. Variance - Correct Answers (∑x²/n) - (∑x/n)²
10.Standard Deviation - Correct Answers √variance
11.Histograms: Height - Correct Answers Area = k x frequency
12.Frequency Density - Correct Answers frequency ÷ class width
13.Population - Correct Answers Whole set of items of interest.
14.Census - Correct Answers Observes/measures every member of a population
15.Sample - Correct Answers Selection of observations taken from a subset of the
population which is used to find out info about the population.
16.Sampling Frame - Correct Answers A list of individuals (named or numbered)
from whom the sample is drawn
17.Random Sampling - Correct Answers Every member of the population has an
equal chance of being selected
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13
pf14
pf15
pf16
pf17
pf18
pf19
pf1a
pf1b
pf1c

Partial preview of the text

Download Excel a Level Math’s – Statistics questions and answers for 2024 candidates and more Exams Mathematics in PDF only on Docsity!

Excel a Level Math’s – Statistics questions

and answers for 2024 candidates

  1. Linear Regression - Correct Answers y = axⁿ
  2. logy = loge + log
  3. Exponential Regression - Correct Answers y = ax
  4. logy = loge + log
  5. Normal Approximation - Correct Answers μ = np
  6. σ =√(np(1-p))
  7. Mean - Correct Answers ∑x ÷ n
  8. GF: ∑of ÷ ∑f
  9. Variance - Correct Answers (∑x²/n) - (∑x/n)²
  10. Standard Deviation - Correct Answers √variance
  11. Histograms: Height - Correct Answers Area = k x frequency
  12. Frequency Density - Correct Answers frequency ÷ class width
  13. Population - Correct Answers Whole set of items of interest.
  14. Census - Correct Answers Observes/measures every member of a population
  15. Sample - Correct Answers Selection of observations taken from a subset of the population which is used to find out info about the population.
  16. Sampling Frame - Correct Answers A list of individuals (named or numbered) from whom the sample is drawn
  17. Random Sampling - Correct Answers Every member of the population has an equal chance of being selected
  1. Systematic Sampling - Correct Answers every nth person is chosen.
  2. Stratified Sampling - Correct Answers Population is divided into mutually exclusive Strat and a random sample is taken from each.
  3. Quota Sampling - Correct Answers Interviewer selects a sample that reflects the characteristics of the population
  4. Opportunity Sampling - Correct Answers Choosing whoever is available
  5. Continuous Variable - Correct Answers Can take any value in a given range
  6. Discrete Variable - Correct Answers Takes specific values in a given range
  7. Conditions for Binomial - Correct Answers Fixed no. of trials
  8. 2 possible outcomes
  9. Outcomes are independent
  10. Fixed probability of success
  11. Probability: Independent if... - Correct Answers P(A∩B) = P(A) X P(B)
  12. P(A|B) = P(A)
  13. Probability: Mutually exclusive if... - Correct Answers P(A∩B) = 0
  14. P(A∪B) = P(A) + P(B)
  15. Conditional Probability - Correct Answers P(A|B) = P(A∩B)/P(B)
  16. Probability Addition Rule - Correct Answers P(A∪B) = P(A) + P(B) - P(A∩B)
  17. If there are 3 events, and A and B are mutually exclusive... - Correct Answers P(A∪B∪C) = P(A) + P(B) + P(C) - P(A∩C) - P(B∩C)
  18. What is a DRV - discrete random variable - Correct Answers it is a random variable that can only take certain values
  19. ... - Correct Answers ...
  20. probability mass function - Correct Answers a function that gives the probability that a discrete random variable is exactly equal to some value
  21. what does a probability distribution do - Correct Answers describes the probability of any outcome in the sample space
  22. P(A/B) = - Correct Answers (P(A n B))
  1. mutually exclusive events - Correct Answers Two events that cannot occur at the same time
  2. what is P(A∩B) if two events are mutually exclusive - Correct Answers P(A∩B) = 0
  3. Sampling units - Correct Answers Individual units of a population
  4. what does a census do - Correct Answers observes and measures every member of a population
  5. advantages / disadvantages of census - Correct Answers advantages :
  6. gives a completely accurate result
  7. disadvantages
  8. -time consuming and expensive
  9. -hard to process large quantity of data
  10. advantages/disadvantages of a sample - Correct Answers advantages :
  11. less time consuming and expensive than census
  12. fewer people have to respond
  13. less data to process than in a census
  14. disadvantages
  15. data may not be as accurate
  16. sample may not be large enough to give information about sub groups of the population
  17. sampling frame - Correct Answers a list of individuals from whom the sample is drawn
  18. population - Correct Answers a whole set of items that are of interest
  19. sample - Correct Answers a selection of observations taken from the subset of the population which is used to find out information about the population as a whole
  20. simple random sampling - Correct Answers Every sample from the population has an equal chance of being chosen
    • formed by when each item given number then random number generator used or lottery
  1. simple random sampling advantages/disadvantages - Correct Answers advantages
  2. -easy and cheap to implement for small populations and small samples
    • free of bias
  3. -each sample unit has a known and equal chance of selection
  4. disadvantages
  5. sampling frame is needed
  6. not suitable when population size/sample size is large as it would be potentially tie consuming, disruptive and expensive
  7. 3 different types of random sampling - Correct Answers Simple random sampling
  8. Systematic sampling
    • Stratified sampling
  9. systematic sampling - Correct Answers The required elements are chosen at regular intervals from an ordered list
  10. e.g. if sample size was 20 out of population of 100 you would take one out of every 5 as 100/20=
  11. advantages/disadvantages systematic sampling - Correct Answers advantages
    • easy and quick to use
    • suitable for large samples/populations
  12. disadvantages
  13. sample frame needed
  14. can introduce bias if sampling frame not random
  15. stratified sampling - Correct Answers a variation of random sampling; the population is divided into mutually exclusive strata - males and females for example
  16. and a random sample is taken from each
  17. number sampled in a stratum/total sample size = number in stratum/number in population
  1. discrete variable - Correct Answers variable that only have set values
  2. class boundaries - Correct Answers Tell you the maximum and minimum values that belong in each class
  3. Class width - Correct Answers the difference between upper and lower class limits. - remember if continuous above 0.5 and below by 0.
  4. words to describe scatter diagrams - correlation - Correct Answers Strong - close points to each other
  5. Weak
  6. Positive
  7. Negative
  8. Fairly
  9. Very
  10. Extremely - how steep
  11. None
  12. how to describe correlations in questions - Correct Answers - always link to question context e.g. house prices go up the closer they are to the station
  13. regression lines - Correct Answers The line of best fit drawn through a scatterplot
  14. they have equation
  15. y=a + box
  16. b is gradient
  17. if positive then they are correlated positively
  18. if negative then negatively correlated
  19. interpolation - Correct Answers estimating a value within the range of measured data
    • USUALLY MORE RELIABLE
  20. You are usually asked to give an interpretation of the gradient
  21. Egg for every 1 degree rise there will be 22 more ice creams sold per hour
  22. For every 1 minute passed the temperature will cool by 1.5 degrees
  23. For every hour passed the bacteria will have increased by 15 - does this seem right? LOOK AT THE SCALE egg 15 (million) they were in millions
  24. Extrapolation - Correct Answers Estimating a value outside the range of measured data.
    • usually unreliable
  1. how to identify outliers - Correct Answers - if it is 1.5*IQR above/below the upper/lower quartiles it is an outlier
    • if it is more than 2 standard deviations from the mean it is outlier
  2. coding - inverse function - Correct Answers means it is the exact inverse function e.g. if the x was formed from 2y+4 you would do x-4 /2 to get x
  3. however for standard deviation it is slightly different
  4. -if standard deviation =b was formed by 3d+8 to get the d you would just divide by 3 and not account for subtracting the 8. - However IT IS ALWAYS POSITIVE VALUE SO IF WORKING BACKWARDS IT COULD BE NEGATIVE OR POSITIVE SO YOU WOULD NEED MEAN INFORMATION TO SOLVE.
  5. variance - Correct Answers standard deviation squared
  6. binomial PD - Correct Answers probability of n successful
  7. binomial CD - Correct Answers probability of 0-n successful cumulative
  8. in binomial distribution for each random variable what must there be - Correct Answers - independent of each other
    • fixed number of trials
    • 2 outcomes
    • fixed probability
  9. how to find which to put on x axis - Correct Answers x always on top or left of graph
  10. uniform distribution - Correct Answers probability of each event exactly same
  11. what is trace in statistics - Correct Answers a specific value which is small
  12. comparing box plots - Correct Answers - Compare Medians
- Compare Range (IQR) - Compare Skew - Put comparison into context
  1. histograms what to know - Correct Answers class width * frequency density = frequency
  2. might need to use ratios
  1. mode - Correct Answers the most frequently occurring score(s) in a distribution
    • pros unaffected by extreme values, easy to calculate
    • cons only useful if there are relatively high frequencies involved
  2. what to remember for doing inverse functions of means and standard deviations - coding - Correct Answers means it is the exact inverse function e.g. if the x was formed from 2y+4 you would do x-4 /2 to get x
  3. however for standard deviation it is slightly different
  4. -if standard deviation =b was formed by 3d+8 to get the d you would just divide by 3 and not account for subtracting the 8
  5. what is variance - Correct Answers How the values are dispersed around the mean; the larger the variance, the larger the dispersion of the scores
  6. what to remember about Jacksonville - Correct Answers really hot - most hot
  7. in southern east coast of America
  8. 23-28 degree average
  9. what to remember about Beijing - Correct Answers temperature relatively high
  10. high temperature range
  11. What to remember about Perth - Correct Answers temperature range similar to UK
  12. It is in Australia
  13. Has some extreme values of data - maximum rainfall 102mm
  14. Near to sea
  15. What to remember about UK - Correct Answers July - August have highest temperatures
  16. 15-16th October 1987 was storm so high wind speeds rainfall etc.
  17. Heathrow is warmest
  18. Lechers coldest
  19. Horn is by sea so more windy
  20. Are there cities that have very different weather to others - Correct Answers Beijing vs lechers
  21. What is UK temp range - Correct Answers 3.8-28.7 degrees Celsius
  1. Which cities are the wettest? - Correct Answers Camborne - 3.4 mm
  2. Jacksonville - 5.9 mm
  3. If you are rolling a dice, when writing a probability mass function after naming the probabilities of 1-6 each with 1/6, what must you state? - Correct Answers must state probability otherwise is 0
  4. driest city in Up - Correct Answers Lemming
  5. difference temp in 2015 vs 1987 - Correct Answers slightly higher temps in 2015
  6. what cloud cover measured in - Correct Answers 0-8 okras
- each 1/9 chance
  1. windiest months 2015 - Correct Answers May in UK and Beijing
  2. -October for Jacksonville
- September for Perth
  1. Binomial Distribution questions
  2. how to answer :
  3. If Ben rolls dice six times and wants to see how many 5s he gets (fair dice), explain the distribution you would use? - Correct Answers - binomial distribution would be use
    • all distributions are modelled with 'X'
    • X~B(nap)
  4. where n is number of trials
  5. p is p(success)
  6. for this question it would be X~B(6,1/6)
  7. Common Binomial Distribution question:
  8. Probability of desired outcome = P
  9. Find the smallest number of weeks/months/rolls/attempts after which it will be - some percentage e.g. 85 percent - certain he has obtained his desired outcome at least once. - Correct Answers how to solve ;
  10. P and percentage as decimal would be either solved/given in question
  11. 1st Method -
  1. How to find LQ - Correct Answers if it is discrete data find 1/4n. If this is a whole number, the lower quartile is half way between this data point and the one above. If it is not a whole number round up and pick this data point.
  2. definition of an outlier - Correct Answers - more than 2 standard deviations from the mean
    • either greater than the UQ by the IQR or lower than LQ by IQR
  3. what is cleaning the data - Correct Answers The process of removing anomalies from a data set
  4. how to calculate the height of each bar[aka the frequency density] what formula you use - Correct Answers area of bar = k * frequency
  5. how to form a frequency polygon from a histogram - Correct Answers - joining the middle of the top of each bar in a histogram forms a frequency polygon
  6. when comparing sets of data what do you comment on - Correct Answers - a measure of location
    • a measure of spread
  7. What is bivariate data? - Correct Answers Data which has pairs of values for two variables
  8. what is correlation - Correct Answers relationship between two variables
  9. what is a regression line - Correct Answers line of best fit , written in form y=box + a
    • if b is positive data is positively correlated
    • if b is negative data is negatively correlated
  10. why do we use regression lines - Correct Answers - to make prediction for values of the dependent variable that are within the range of the given data
  11. purpose of a Venn diagram - Correct Answers - represents events graphically
    • frequencies or probabilities can be placed in the regions of the Venn diagram
  13. if events are mutually exclusive what does P[A OR B] = - Correct Answers P[A OR B] = P[A] + P[B]
  1. If events are independent what does P[A and B]= - Correct Answers P[A]
* P[B]
  1. What is the purpose of a tree diagram? - Correct Answers - shows the outcome of two or more events happening in succession
  2. what is the purpose of a probability distribution - Correct Answers - describes the probability of any outcome in the sample space
  4. what does ∑P[X=x] equal for all events - Correct Answers ∑P[X=x] = 1
  5. How to know whether you can model X with a binomial distribution B[nap] - Correct Answers there has to be :
    • a fixed number of trials , n
    • two possible outcomes , success or failure
    • fixed probability of success , p
    • the trials are independent of one another
  6. what does n and p mean in binomial distribution B[nap] - Correct Answers n, the first part is the fixed number of trials
  7. p ,the second part is the fixed probability of success
  8. If random variable X has the binomial distribution B[nap] what is its probability mass function given by - Correct Answers P[X=x] = [n pox[1-p]^n-x
  9. x]
  10. What is the null hypothesis H0? - Correct Answers The hypothesis you assume to be correct
  11. What is the alternative hypothesis H1? - Correct Answers The hypothesis that tells us about the parameter if your assumption is chosen to be wrong.
  12. What are one tailed tests? - Correct Answers they are hypothesis tests with an alternative hypothesis in the form H1: p<... and H1: p>...
  13. What are two tailed tests? - Correct Answers they are hypothesis tests with an alternative hypothesis in the form H1: p≠...
  14. What is a critical region? - Correct Answers A region of the probability distribution which, if the test statistic falls within it, would cause you to reject the null hypothesis
  • options
  • number 3
  • then it will tell you r
  1. What can PMCC can also be written - Correct Answers r
  2. When you are doing a binomial distribution rules what to remember - Correct Answers 1. If it is more than one number you use CD
    1. If it is one exact number you use PD
    1. if it is more than a certain number of trials, n or greater you cannot use this in your calculator and instead ,using CD you use n-1 in calculator then do 1- [that probability calculated]
    1. If it was calculate probability more than n you would use CD in your calculator with n then do 1-[probability calculated]. This is because greater than n is the same as greater than or equal to n+1 which is the same as less than or equal to n.
  6. And the calculator can only use n in format less than equal to.
  7. what is the complement of A - Correct Answers A'
  8. if two events are independent events what does P[A|B] = - Correct Answers P[A|B] = P[A]
  9. what is the area under a continuous probability distribution equal to: - Correct Answers it is equal to one
  10. difference between Binomial distribution and the normal distribution - Correct Answers BD is discrete values
  • ND is continuous values
  1. in normal distribution X~N[μ,variance] what is μ and variance - Correct Answers μ is population mean
  2. variance is standard deviation squared
  3. facts about the normal distribution - Correct Answers - has parameters μ , the population mean, and the variance
  • is symmetrical - mean=median=mode
  • has bell shaped curve with asymptotes at each end
  • total area 1
  1. -points of inflection at μ + standard deviation and μ - standard deviation
  • mean is 0
  • 68 percent of data lies within one standard deviation of the mean
  • 95% data lies within 2 standard deviations of the mean
  • 99.7% lies within three standard deviations of the mean
  1. how is the standard Normal variable written as - Correct Answers written as Z-N[0,1^2]
  2. If n is large and p is close to 0.5 then the binomial distribution how can X~B[nap] can be approximated by the normal distribution - Correct Answers X~B[nap] can be approximated by the normal distribution where
  3. μ = np
  4. standard deviation = √[np[1-p]]
  5. what do you have to remember to do when using a normal approximation to a binomial distribution - Correct Answers - you need to apply a continuity correction when calculating probabilities
  6. For a random sample of size n taken from a random variable X~N[μ,variance] , how is the sample mean normally distributed as - Correct Answers sample mean = X[BAR] ~N[μ,variance/n]
  7. for the sample mean of a normally distributed random variable X[BAR] ~N[μ,variance/n] what does Z =
  8. where Z~N[0,1] - Correct Answers Z = [Bar -μ] / [standarddev/√n]
  9. whats is μ - Correct Answers population mean
  10. examples of variables that can be modelled using the normal distribution - Correct Answers - heights of people in given population
    • weights of tigers in jungle
    • errors in scientific measurements
    • size measurements of manufactured objects
  11. Finding probability of more or less than something using Normal distribution - Correct Answers 1. Load up number 7 and choose normal CD [2]
    1. Draw Bell shaped curve and shade region you want to find
    1. Then if asking you for P [X> A] set lower limit to A and Upper limit as a very large number e.g. 10000000
    1. If asking P[X<A] set upper limit to A then lower to very low number e.g. - 1000000
    1. If asking P[A<X<B] Then set A as upper and B as lower
    1. If asking P[XB] then find probabilities separately like before and add them
    1. Obviously put in standard deviation which is root variance then population mean
    1. take answer *100 for percentage
  • you could be asked to μ
  1. HARDER VERSION :
  2. -You may be given two unknowns e.g. μ and σ
  • But it will give you two areas so e.g.
  1. you would solve to get [75 - μ]/σ =Φ^-1[0.7]
  2. and [85-μ]/σ = Φ^-1[0.33] then you would solve as a simultaneous equation
  3. Hypothesis testing with the normal distribution - what to remember about how mean and standard deviation are affected using sample size n - Correct Answers - For a random sample of size n taken from a random variable Xin(μ,σ²) , the sample X(bar)~N(μ,σ²/n)
  • TO NOT σ²/n IS YOUR NEW σ² NOT JUST STANDARD DEVIATION
  1. What is a null hypothesis? - Correct Answers Originally stated hypothesis , H
  2. What is alternative hypothesis? - Correct Answers What we are testing to see if true ,H
  3. What is a one-tailed test? - Correct Answers One-tailed test: tests whether the value is greater than OR less than a given number in H
  • Use full significance (e.g. 5%)
  1. what is a two tailed test - Correct Answers Two-tailed test: tests whether a parameter is equal to a given number or not given for H
  • REMEMBER THAT IF NEW MEAN GIVEN IN THE QUESTION IS LESS THAN ORIGINAL MEAN FOR H0 GIVEN FOR SAMPLE SIZE N , THEN YOU TEST THE PROBABILITY IN YOUR CALC BY DOING P(X>NEW X MEAN) AND IF ORIGINAL MEAN IS MORE YOU DO P(X<NEW MEAN) USING POPULATION MEAN AS MEAN IN H0 AND NEW STANDARD DEVIATION CALCULATED BY σ²/N
  • draw curve to understand this more
  • You are essentially testing the new mean
  • see notes
  • you need to half the significance (e.g. 2.5%) as you are testing either side
  1. When do we accept the null hypothesis? - Correct Answers when the percentage calculated using either one tailed or two tailed test is more than the level of significance stated in the question
  1. When do we accept the alternative hypothesis? - Correct Answers when the percentage calculated using either one tailed or two tailed test is less than the level of significance stated in the question
  2. How to solve a Hypothesis /level of significance question for the normal Distribution - Correct Answers - DRAW CURVE TO UNDERSTAND BETTER
  3. -Model X(BAR) - new variable(sample mean) as normal distribution using same μ as before but remembering divide variance by n sample size
    • you should be given original μ and the σ² which you have to divide by n to get new σ² -
  4. -YOU USE ASSUMED MEAN GIVEN AS H
- *Write Your H1 and H0s out* - to find probability go into calculator type in normal CD , then for two tailed test if new sample mean is greater than H0 put lower limit as new sample mean and upper as large number / vice versa if H0 is greater. Then have SD as the SD^2/N and the mean as the original H0 then calculate number and compare to 0. - to find probability of one tailed test it should be clear as you already know which side it lies on (just draw graph) - Now change this probability to a percentage
  1. and compare it with significance level described in question
- if percentage calculated greater than it is insignificant and accept H0 and if less than it is significant and accept H - State whether it is insignificant or not and which hypothesis you are accepting in question
  1. IMPORTANT NOTE :
  2. If it is two tailed test you are comparing percentage calculated to half the significance level stated in the question
  3. If you have calculated value b for probability normal distribution of X(bar) with sample size n ,using hypothesis testing in a two tailed test - what do you compare this with to determine whether it is significant or not and whether one should accept or reject H0 - Correct Answers - you compare value b to half of significance value stated in question ONLY FOR TWO TAILED - IF IT WAS ONE TAILED YOU USE SIGNIFICANCE STATED IN ORIGINAL QUESTION
  4. What is Bar in hypothesis testing - Correct Answers - X bar is new X variable
  5. Way to know whether you are testing above or below value for two tailed hypothesis test - Correct Answers - well draw the graph