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Statistics Please choose a question to attempt from the following: 1 EXIT 2 3 4 Back to Unit 2 Menu 5 STATISTICS : Question 1 A taxi company was phoned each night of the week and the response time in minutes of their cars were noted. They were …. 35 10 7 7 15 9 (a) Find the mean and standard deviation for this data. (b) A similar experiment was conducted with a second company. The results for this were…. mean = 12 and standard deviation = 1.88 How does the second company compare to the first? Get hint Reveal answer only Go to full solution EXIT Go to Comments Go to Statistics Menu STATISTICS : Question 1 A taxi company was phoned each night of the week and the response time in minutes of their cars were noted. They were …. 35 (a) SD (b) EXIT 10 15 9 Draw a7table 7 n data deviation for this data. 2 comparing Find the mean and standard mean x x to mean. Then square A similar experiment was conducted with a second n Thevalues. company. results for this were…. n 1 When comparing data sets= always mean = 12 and standard deviation 1.88 make comment on How does the second companythe compare to(which the first? average is bigger etc.) and the spread of the data. Reveal answer only Go to Comments Go to full solution Go to Statistics Menu What would you like to do now? STATISTICS : Question 1 A taxi company was phoned each night of the week and the response time in minutes of their cars were noted. They were …. 35 10 7 7 15 9 (a) Find the mean and standard deviation for this data. (b) A similar experiment was conducted with a second company. The results for this were…. mean = 12 and standard deviation = 1.88 How does the second company compare to the first? (a) Mean = 8 SD 3.87 (b)The second company has a longer average response time. The smaller standard deviation means their arrival time is more predictable. Go to Comments What would you like to do now? EXIT Go to full solution Go to Statistics Menu Question 1 A taxi company was phoned each night of the week and the response time in minutes of their cars were noted. They were …. 3 5 10 7 7 15 9 (a) Find the mean and standard deviation for this data. Begin Solution Continue Solution Comments Statistics Menu Back to Home 1. Calculate mean. (a) Mean = (3+5+10+7+7+15+9)7 = 8 So x = 8 and no.pieces of data = n = 7 Question 1 A taxi company was phoned each night of the week and the response time in minutes of their cars were noted. They were …. 3 5 10 7 7 15 9 (a) Find the mean and standard deviation for this data. x 8 Begin Solution Continue Solution Comments Statistics Menu Back to Home 2. Draw table comparing data to mean. x 3 5 10 7 7 15 9 -5 -3 2 -1 -1 7 1 25 9 4 1 1 49 1 (x - x )2 = 90 xx xx 2 Question 1 A taxi company was phoned each night of the week and the response time in minutes of their cars were noted. They were …. 3 5 10 7 7 15 9 (a) Find the mean and standard deviation for this data. Begin Solution Continue Solution Comments Statistics Menu Back to Home 3. Use formula to calculate standard deviation. xx SD n 1 90 SD 6 SD 3.87 2 Just found!! Question 1 (b) A similar experiment was conducted with a second company. The results for this were…. mean = 12 and standard deviation = 1.88 How does the second company compare to the first? x 8 1. Always compare mean and standard deviation. (b)The second company has a longer average response time. The smaller standard deviation means their arrival time is more predictable. SD 3.87 What would you like to do now? Begin Solution Continue Solution Comments Statistics Menu Back to Home Comments 3. Use formula to calculate standard deviation. xx SD n 1 90 SD 6 SD 3.87 2 Check the list of Formulae for the Standard Deviation Formula: ( x x) n 1 2 or 2 ( x ) x 2 n n 1 The second formula can be used in the calculator paper. The calculator must be in Stats. Mode to allow the data to be entered. Next Comment Statistics Menu Back to Home STATISTICS : Question 2 Weeks of training A TV personality takes part in a 20 week training schedule to copy a 100m sprinter. Her times are recorded every 2 weeks and plotted in the graph then a line of best fit is drawn. EXIT Continue question STATISTICS : Question 2 Get hint Reveal answer only Go to full solution Go to Comments Go to Stats Menu Weeks of training (i) Find the equation of the line in terms of T and W. (ii) Use answer (i) to predict (a) her time after 12 weeks of training (b) the week when her time was 11.5secs EXIT STATISTICS : Question 2 Find gradient Use Use your your and note intercept equation equation and and of T axis. substitute substitute WT= =12. 11.5 Reveal answer only Go to full solution Go to Comments Go to Stats Menu Weeks of training (i) Find the equation of the line in terms of T and W. (ii) Use answer (i) to predict (a) her time after 12 weeks of training (b) the week when her time was 11.5secs EXIT What would you like to do now? STATISTICS : Question 2 What would you like to do now? Go to full solution Go to Comments Go to Stats Menu Weeks of training (i) Find the equation of the line in terms of T and W. (ii) Use answer (i) to predict EXIT T = -¼ W + 15 (a) her time after 12 weeks of training 12secs. (b) the week when her time was 11.5secs 14 weeks Question 2 (i) Find the equation of the line in terms of T and W. 1. Find gradient and note intercept of T axis. (a) m = (y2 – y1) 10 - 15 = -¼ = (x2 – x1) 20 - 0 Intercept at 15 Equation is Go to graph Begin Solution Continue Solution Comments Statistics Menu Back to Home T = -¼ W + 15 Question 2 (ii) Use answer (i) to predict (a) her time after 12 weeks of training (b) the week when her time was 11.5secs 2. Use your equation and substitute W = 12. (b)(i) If w = 12 then T = -¼ W + 15 becomes T = (-¼ x 12) + 15 = -3 + 15 = 12 Time at 12 weeks is 12secs. Begin Solution Continue Solution Comments Statistics Menu Back to Home Question 2 (ii) Use answer (i) to predict (a) her time after 12 weeks of training (b) the week when her time was 11.5secs 3. Use your equation and substitute T = 11.5 (b)(i) If t = 11.5 then becomes T = -¼ W + 15 -¼ W + 15 = 11.5 (-15) (-15) -¼ W = -3.5 x (–4) W = 14 Reach a time of 11.5sec after 14 weeks. What would you like to do now? Begin Solution Continue Solution Comments Statistics Menu Back to Home Comments 1. Find gradient and note intercept of T axis. (a) m = (y2 – y1) 10 - 15 = -¼ = (x2 – x1) 20 - 0 To find the equation of a line from the graph: Must Learn: y = mx + c Intercept at 15 Equation is T = -¼ W + 15 gradient intercept So you need to find these!! Next Comment Statistics Menu Back to Home Comments 1. Find gradient and note intercept of T axis. (a) m = (y2 – y1) 10 - 15 = -¼ = (x2 – x1) 20 - 0 vertical m = horizontal Note: Always draw the horizontal before the vertical: Intercept at 15 horizontal (+ve) Equation is T = -¼ W + 15 vertical (-ve) Next Comment Statistics Menu Back to Home STATISTICS : Question 3 A sample of 180 teenagers were asked their opinions on the TV series the “Simpsons” & the movie “Shrek” and their responses were displayed in the following table… Like Don’t like Simpsons Like Shrek Don’t like Shrek Simpsons 126 ? 15 21 (a) What percentage liked Shrek but not the Simpsons? (b) If someone is picked at random what is the probability that (i) they liked the Simpsons but not Shrek? (ii) they liked neither? Get hint EXIT Reveal Full solution Comments Statistics Menu STATISTICS : Question 3 A sample of 180 teenagers were asked their opinions on the TV series the “Simpsons” & the movie “Shrek” and their responses were displayed in the following table… Like Don’t like Simpsons Like Shrek Don’t like Shrek 126 15 Simpsons Remember To find probabilities all entries in use: ? P = no oftable must add to total favourable / no of sample size data 21 (a) What percentage liked Shrek but not the Simpsons? (b) If someone is picked at random what is the probability that (i) they liked the Simpsons but not Shrek? (ii) they liked neither? EXIT What would you like to do now? Full solution Statistics Menu Comments Reveal STATISTICS : Question 3 A sample of 180 teenagers were asked their opinions on the TV series the “Simpsons” & the movie “Shrek” and their responses were displayed in the following table… Like Don’t like Simpsons Like Shrek Don’t like Shrek Simpsons 126 ? 15 21 (a) What percentage liked Shrek but not the Simpsons? 10% (b) If someone is picked at random what is the probability that (i) they liked the Simpsons but not Shrek? (ii) they liked neither? Full solution EXIT Comments 7/ 60 Statistics Menu What now? 1/ 12 Question 3 1. Use P = no of favourable / no of data Like Simpsons Like Shrek Don’t like Shrek Don’t like Simpsons 126 ? 15 21 (a) What percentage liked Shrek but not the Simpsons? Begin Solution Continue Solution Comments Statistics Menu Back to Home NB: There are 180 in survey!! (a) Like Shrek but not Simpsons = 180 – 126 – 15 – 21 = 18 % = 18/180 = 1/ 10 = 10% Question 3 1. Use P = no of favourable / no of data Like Simpsons Like Shrek Don’t like Shrek Don’t like Simpsons 126 ? 15 21 what is the probability that (i) they liked the Simpsons but not Shrek? Begin Solution Continue Solution Comments Statistics Menu Back to Home (b)(i) Prob = 15/ 180 = 1/ 12 Question 3 1. Use P = no of favourable / no of data Like Simpsons Like Shrek Don’t like Shrek Don’t like Simpsons 126 ? 15 21 (b)(ii) Prob = 21/ 180 = 7/ 60 What would you like to do now? (ii) they liked neither? Begin Solution Continue Solution Comments Statistics Menu Back to Home Comments 1. Use P = no of favourable / no of data NB: There are 180 in survey!! (a) Like Shrek but not Simpsons Note: To change a fraction to a % multiply by 100% 18 180 = 18 180 x 100% = 180 – 126 – 15 – 21 = 18 % = 18/180 = 1/ 10 = 10% Next Comment Statistics Menu Back to Home Comments To calculate simple probabilities: 1. Use P = no of favourable / no of data Probability = (b)(i) Prob = 15/ 180 = 1/ 12 Number of favourable outcomes Number of possible outcomes Next Comment Statistics Menu Back to Home STATISTICS : Question 4 Get hint On a college course you have to pick a language plus a Reveal ans leisure activity from the following lists LANGUAGE FRENCH GERMAN SPANISH LEISURE MUSIC VIDEO PRODUCTION BASKETBALL SWIMMING Full solution Comments Stats Menu (a) Make a list of all possible combinations of courses. (b) If a combination is selected at random what is the probability that it is …… (i) Includes Spanish? (ii) Includes swimming? EXIT (iii) Doesn’t include French but includes music? What would you like to do now? STATISTICS : Question 4 On a college course you have to pick a language plus a Reveal ans leisure activity from the following lists LANGUAGE FRENCH GERMAN SPANISH LEISURE MUSIC VIDEO PRODUCTION BASKETBALL SWIMMING Full solution Comments Stats Menu (a) Make a list of all possible combinations of courses. Use a tree diagram & “branch (b) If a combination is selected at random what is the Now list out” with probability that it is …… the pairs each Use your From list eachof of language. language “branch (i) Includes Spanish? possible subjects. out” with each combinations to find (ii) Includes swimming? leisure activity. probabilities. EXIT (iii) Doesn’t include French but includes music? STATISTICS : Question 4 On a college course you have to pick a language plus a leisure activity from the following lists LANGUAGE FRENCH GERMAN SPANISH Full solution LEISURE MUSIC VIDEO PRODUCTION BASKETBALL SWIMMING (a) Make a list of all possible combinations of courses. Comments Stats Menu CLICK (b) If a combination is selected at random what is the probability that it is …… (i) Includes Spanish? (ii) Includes swimming? EXIT 1/ 3 1/ 4 1/ (iii) Doesn’t include French but includes music? 6 (a) French/Music French/Video French/Bsktbll French/Swim German/Music GERMAN German/Video German/Bsktbll German/Swim Spanish/Music Spanish/Video Spanish/Bsktbll Spanish/Swim Hints Use a tree diagram & “branch out” with each language. From each language “branch out” with each leisure activity. Now list the pairs of subjects. Hints French/Music Have list of combinations handy. French/Video French/Bsktbll (b)(i) Prob = 4/12 = 1/ 3 Remember to simplify. French/Swim What now? German/Music German/Video Comments (b)(ii) Prob = 3/12 = 1/ 4 Stats Menu German/Bsktbll What is probability: German/Swim (i) Includes Spanish? Spanish/Music Spanish/Video Spanish/Bsktbll Spanish/Swim (ii) Includes swimming? (b)(iii) Prob = 2/12 = 1/6 (iii)Doesn’t include French but includes music? Comments (a) French/Music French/Video No. of possible outcomes French/Bsktbll French/Swim GERMAN = 3 x 4 = 12 German/Music To calculate simple probabilities: German/Video Probability = German/Bsktbll German/Swim Number of favourable Number of possible Spanish/Music Spanish/Video Spanish/Bsktbll Next Comment Spanish/Swim Statistics Menu Back to Home STATISTICS : Question 5 The delivery times for a fast food company are shown in the following cumulative frequency table. Time No. Deliveries up to 4 mins up to 8 mins up to 12 mins 5 13 37 up to 16 mins up to 20 mins 53 60 Get hint Reveal ans Full solution Comments Stats Menu (a) How many deliveries took longer than 16 mins? (b) Use the data to construct a cumulative frequency graph. (c) Use the graph to find the median and semi-interquartile range for this data. STATISTICS : Question 5 The delivery times for a fast food company are shown in the following cumulative frequency table. What would you like to do now? For how many Time greater than Median is 16 up findto 4 mins middle difference valueso 8we up to mins between end SIQR = ½(Q3 – Q1) want value of up to 12 mins halfwayvalues to point & Q1up – 25% point on up–to 16point mins 16. Q3 75% frequency up to 20 mins axis. No. Deliveries 5 13 37 53 60 Reveal ans Full solution Comments Stats Menu (a) How many deliveries took longer than 16 mins? (b) Use the data to construct a cumulative frequency graph. (c) Use the graph to find the median and semi-interquartile range for this data. STATISTICS : Question 5 The delivery times for a fast food company are shown in the following cumulative frequency table. Time No. Deliveries up to 4 mins up to 8 mins up to 12 mins 5 13 37 up to 16 mins up to 20 mins 53 60 Full solution Comments Stats Menu =7 (a) How many deliveries took longer than 16 mins? (b) Use the data to construct a cumulative frequency graph. (c) Use the graph to find the median and semi-interquartile range for this data. Median = 11 mins SIQR = 2.75 mins (a) Deliveries taking longer than 16 mins = 60 – 53 = 7 Time Deliveries Cum freq 4 5 ¾ of 60 = 45 Q3 Q2 8 13 12 37 Comments ½ of 60 = 30 16 53 20 60 Stats Menu ¼ of 60 = 15 What would you like to do now? Q1 8.5 (C) Median = 11mins. 11 14 Delivery time(mins) (c) SIQR = ½(Q3 – Q1) = (14 – 8.5) 2 = 2.75mins Comments Note: In a Cumulative Frequency Diagram: Cumulative Frequency On y-axis (cumulative frequency) 60 Q1 at 25%, 50% Q2 at 50%, Q3 at 75% 11 20 Delivery Time And read values from the delivery time scale (x-axis). End of Statistics Next Comment Statistics Menu Back to Home