Download in
Google Play
Infection and response
Organisation
Cell biology
Biological molecules
Homeostasis and response
Responding to change (a2 only)
Energy transfers (a2 only)
The control of gene expression (a-level only)
Substance exchange
Bioenergetics
Genetic information & variation
Inheritance, variation and evolution
Genetics & ecosystems (a2 only)
Ecology
Cells
Show all topics
1f industrialisation and the people: britain, c1783-1885
1c the tudors: england, 1485-1603
Britain & the wider world: 1745 -1901
Inter-war germany
World war one
2n revolution and dictatorship: russia, 1917-1953
World war two & the holocaust
1l the quest for political stability: germany, 1871-1991
The cold war
2j america: a nation divided, c1845-1877
Medieval period: 1066 -1509
The fight for female suffrage
2m wars and welfare: britain in transition, 1906-1957
2d religious conflict and the church in england, c1529-c1570
Britain: 1509 -1745
Show all topics
14/06/2023
386
21
Share
Save
Register
Access to all documents
Join milions of students
Improve your grades
By signing up you accept Terms of Service and Privacy Policy
Register
Access to all documents
Join milions of students
Improve your grades
By signing up you accept Terms of Service and Privacy Policy
Register
Access to all documents
Join milions of students
Improve your grades
By signing up you accept Terms of Service and Privacy Policy
Register
Access to all documents
Join milions of students
Improve your grades
By signing up you accept Terms of Service and Privacy Policy
Register
Access to all documents
Join milions of students
Improve your grades
By signing up you accept Terms of Service and Privacy Policy
Register
Access to all documents
Join milions of students
Improve your grades
By signing up you accept Terms of Service and Privacy Policy
Register
Access to all documents
Join milions of students
Improve your grades
By signing up you accept Terms of Service and Privacy Policy
Register
Access to all documents
Join milions of students
Improve your grades
By signing up you accept Terms of Service and Privacy Policy
Register
Access to all documents
Join milions of students
Improve your grades
By signing up you accept Terms of Service and Privacy Policy
Register
Access to all documents
Join milions of students
Improve your grades
By signing up you accept Terms of Service and Privacy Policy
Mean χ = Σχ и x = sum of all observation 'n' number of calculating mean from frequency table x2 n 3 ni 1₂ 2 observation Median calculater turn on frequency setup £3-on statistics 6 OPT - x mean f how many upper Quartile Qg³ middle of higher middle or set of data -median Q₂/position (addi number of observation + +1)/2 nth value Lower Quartile Q₁: middle of lowest - median Q3 Q₁ IQR times In occurs media cumulative frequency_ 3 145-155 ISS -165 9 165-175 21 165 ≤ ≤ 175 cumulative 33 25 3 145 frequency! 155 165 175 median. h 170-175 175-180 180-190 р по-qaps S means 170 <h² 175 175 ≤ ≤180 180 ≤ ≤ 190 width S 10 cumulative 3 amulative (4) 2 grouped frequency, intervals, widths и 170-174 175-179 180-189 frequency density = 12 33 2 3+9 gaps for histograms midpoint of interval lower + upper 2 7h (cm) J11 +21 -0.5 169.5 174.5 174.5 179.5 179.5 ≤189.5 10 frequency class width 10- 20 20-25 25-35 35-50 O ( 2 3 Finding median, quartiles, percentiles from grouped frequency + cumulative frequency 4 ม 5 6 7 8 U= 3853 Standart deviation G measure of spread. 2 {(x₁ - x)² n 0=1 ≤ x² и 12 17 stem and beat diagrams Sorting unsorted data 812=82 20 -z² LB 4+ Standart deviation . Median: Q2 20 10 Interval 20 -25 4 lowest Q2-20 10-4 Q calculater setup turn frequency on ↓3 1 Menu 6 -1- OTPA Q₁ BOX & Whisner plot 2 Q2 25385 10 12 VB Ut = 10 from frequency tables = 25-20 12-4 Q3 highes symmetrical cu. frequency 0-9 18 10-14 14 15-19 16 20-24 15 25-34 17 35-50 10 Histograms -0.5 (when gaps) f. density td2 fal height & width CWI h hi h₂ 41 ها CW I 02 tal frequency density: +02 cWi CW 2 42 ✓ (+) (class width) frequency concinves data group unit Ratio equations negative SROW ㅏ CU. trequency outlier : 01 -1.5( Q3-Q₁) IQR positive skew QB- 1.5(Q₂-Q₁) IQR tree diagrams INPENDENT EVENT • one event unattected by the previous Y 2 P (B) P(8) Prooting independence of events : Y -N -Y P(LIB) P(L1B) P(AMB) = PCA) XP(B) conditional probability Find probability given another event has occured N P(4/6) DEPENDENT TREE DIAGRAMS is attected by what happened. in previous P(RIR) P(416¹) one event occurs another occurs P(A/B) ↓^ given that i got R getting R = P both occur P (given event) P(ANB) P(B) venu diagrams A A-ANB AMB Algebraic type: A A-xx B-AMB A NB АЛВЛС B-x A -x + x + B = x +R=" u = n B B R с R B X Ø A A Shading...
Average app rating
Pupils love Knowunity
In education app charts in 11 countries
Students have uploaded notes
iOS User
Philip, iOS User
Lena, iOS user
regions (AUB)' AUB ven diagrams notations B. A'nBn C A B BO B ل B B A UB A union B everything in а от в от кони A Алв A intersection B Everthing in A and B A' Everything not in A BCA AD B A complement (A MB)¹ B A OO D Алв B¹ (AMB)UC A B is a subset of A A contains B с ANBI A (AUB) B B B с B J A conditional probability in venn diagrams ex ampe es: AMB P (B) ANB P(A) P(AUB) Mutually exclusive Events B P(AUB) PC A/B) P (BIA) A A = P(AUB) = P(A) + P(B) - P(AMB) 3 7 3/5 Yes no x (y) Z PROOF: P(A) + P(B) -(PNB) = P(x+y)+ P(y+z) - p(y) = x+y + y + z -y +2 x +y B 7 = P Using two way tables with probability Girl 4 PLANB) = P(A)XP (BIA)) (P(ANB) = P(A) P(B¹ | A)) Boy 3 5 4 P (AUB 8 P(A/B) = P(BIA) = = 12 % 19 probability laws and Definitions Dependent events: old O15 = mutually venn diagram independent events ↳ unettected PL BIA) = P(B) P(ANB) = P(A) P(B) LD ³2 P(AIB) = ²/1/₂2 1 PC BIA) = ²/3 2 proot that 2 events are independent exclusive cannot occur at the time P(ANB)=0 :: PC AUB) = P(A) + P(B) A W General P(AUB) = P(A) +P(B)-P(ANB) mutually exclusive events two events cannot happen at the same time P(ANB) = O P(AUB) = P(A) +P(B) A B FOO probability Distribution table let X = x . 1 P(X₂)X₁ 4 properties: 2 3 Binomial Distribution X₂ X3 fixed number of trials. · two outcomes, success/failure →CD Binomial trious are independent Probability of success (p) remains constant cumulative Binomial mode 7 A add up to I example P(z ≤6) ▾ CD > P(x ≤7) = P(≤6) distribution P(x≤ x) for X²B(U,P) probability function: P(X+x) = { K (x+2)₂ X=1₁2 1 x = 3,4 P ( X = 1) + P(x =2) +P(x= 3) + P(x=4) = 1 3K 4n e.g P(X=2) Example: P(x² 7) = 1- P(x≤6) P(26) = 1 - P(Z = 6) P(3525) P(x=s) - P(x²2) Binomial Distribution - cumulative Probability tables + + 3к +4к 2 3 % % at least 2 p=0.08 n = IS 3/14 4. 14 к 90% chance of tottees - p= 0.9 bags - и - 20 20 xnB( 20,0.9) PD (x = 20) - 0.122 6(x>18) PD (x = 19) 14 XnB CIS, (x-2) - 0.392 0.08) = 1 = A = /14 1- (x=1) Binomial Distribution - Mean, variance хив (и,р), up mean variance = иря, where ✓ failure Normal Distribution. M x ~ N(№, o) Normal CD (a<x< b) Example: success M 249 250 251.S Normal CD: for xvN (N₁0²) The volume of coffee dispensed from a maschine x mi, is modelled by x^N ( 250, 1.2²) a.) P(249 x 251.5) b.) (x>247.8) B lower : 249 upper : 251.5 0 : 1.2 M : 250 - кр (1,0²) Z = X-N O Inverse Normal Distribution 3 INVERSE NORMAL x^N(N₁0²) P(x<x) X Standart Normal Distribution z ~ N(0,1). 2 BNN (0.1) ↑ > z 2478 250 60 or 999 for upper bound Inverse Area ↓ find z ↓ solve simultanous equations 251) C.) P(x c lower bound -999 2 = x-μ 0 Correlations scatter diagrams r = 0 X Pearson's product moment correlation coefficient r y 1 2 3 S 1 3 6 8 O → no correlation O [= -1 0 x O linear (= -1 positive sa perfect negative whear correlation sa calculater: Statistics mode Menu - 6 - 2 negative a =-0-37 b = 1.77 r. 0.973 y = -0.4 +1.8% T= 1 [=1 → y = a + bx +4 round to I dp. → -close to one no correlation perfect positive Whear correlation sa line of best fit Normal approx to the Binomial Distribution symmetrical 2 ~N[ up, > пря) continvety correction P(Z <16) → • (x < 15.5) no = P(x = 29) → P ( x < 29.5) H PF P(x>28) → P(x> 28.5) A