1. INTERMEDIATE 2 – ADDITIONAL QUESTION BANK UNIT 2 : Statistics You have chosen to study: Please choose a question to attempt from the following: 1 EXIT Back to Unit 2 Menu 2345

2. STATISTICS : Question 1 Go to full solution Go to Comments Go to Statistics MenuReveal answer only EXIT A taxi company was phoned each night of the week and the response time in minutes of their cars were noted. They were …. 351077159 (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

3. STATISTICS : Question 1 Go to full solution Go to Comments Go to Statistics Menu Reveal answer only EXIT A taxi company was phoned each night of the week and the response time in minutes of their cars were noted. They were …. 351077159 (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? Draw a table comparing data to mean. Then square values. When comparing data sets always make comment on the average (which is bigger etc.) and the spread of the data. What would you like to do now?

4. (b)The second company has a longer average response time. The smaller standard deviation means their arrival time is more predictable. STATISTICS : Question 1 Go to full solution Go to Comments Go to Statistics Menu EXIT A taxi company was phoned each night of the week and the response time in minutes of their cars were noted. They were …. 351077159 (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 What would you like to do now?

5. Comments Begin Solution Continue Solution Question 1 Statistics Menu Back to Home 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. (a) Mean = (3+5+10+7+7+15+9)  7 = 8 1.Calculate mean. So = 8 and no.pieces of data = n = 7

6. Comments Begin Solution Continue Solution Question 1 Statistics Menu Back to Home 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. 2. Draw table comparing data to mean. x 3 -5 25 5 -3 9 10 2 4 7 - 1 1 15 7 49 9 1 1  (x - ) 2 = 90

7. Comments Begin Solution Continue Solution Question 1 Statistics Menu Back to Home 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. 3. Use formula to calculate standard deviation. Just found!!

8. Comments Begin Solution Continue Solution Question 1 Statistics Menu Back to Home 1. Always compare mean and standard deviation. (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? (b)The second company has a longer average response time. The smaller standard deviation means their arrival time is more predictable. What would you like to do now?

9. Comments Statistics Menu Back to Home Next Comment 3. Use formula to calculate standard deviation. Check the list of Formulae for the Standard Deviation Formula: The second formula can be used in the calculator paper. The calculator must be in Stats. Mode to allow the data to be entered.

10. STATISTICS : Question 2 EXIT Weeks of training Time(s) 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. Continue question

11. STATISTICS : Question 2 Go to full solution Go to Comments Go to Stats Menu Reveal answer only EXIT Get hint Weeks of training Time(s) (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

12. (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 Use your equation and substitute W = 12. STATISTICS : Question 2 Go to full solution Go to Comments Go to Stats Menu Reveal answer only EXIT Weeks of training Time(s) Find gradient and note intercept of T axis. Use your equation and substitute T = 11.5 What would you like to do now?

13. STATISTICS : Question 2 Go to full solution Go to Comments Go to Stats Menu EXIT Weeks of training Time(s) (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 T = -¼ W + 15 12secs. 14 weeks What would you like to do now?

14. Comments Begin Solution Continue Solution Question 2 Statistics Menu Back to Home 1.Find gradient and note intercept of T axis. (i) Find the equation of the line in terms of T and W. Go to graph m = (y 2 – y 1 ) (x 2 – x 1 ) (a)10 - 15 20 - 0 = Intercept at 15 Equation isT = -¼ W + 15 = -¼

15. (ii) Use answer (i) to predict (a) her time after 12 weeks of training (b) the week when her time was 11.5secs Comments Begin Solution Continue Solution Question 2 Statistics Menu Back to Home 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.

16. (ii) Use answer (i) to predict (a) her time after 12 weeks of training (b) the week when her time was 11.5secs Comments Begin Solution Continue Solution Question 2 Statistics Menu Back to Home 3. Use your equation and substitute T = 11.5 (b)(i) If t = 11.5 then T = -¼ W + 15 becomes -¼ W + 15 = 11.5 (-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?

17. Comments Statistics Menu Back to Home Next Comment 1.Find gradient and note intercept of T axis. m = (y 2 – y 1 ) (x 2 – x 1 ) (a)10 - 15 20 - 0 = Intercept at 15 Equation isT = -¼ W + 15 = -¼ To find the equation of a line from the graph: Must Learn: y = mx + c gradientintercept So you need to find these!!

18. Comments Statistics Menu Back to Home Next Comment 1.Find gradient and note intercept of T axis. m = (y 2 – y 1 ) (x 2 – x 1 ) (a)10 - 15 20 - 0 = Intercept at 15 Equation isT = -¼ W + 15 = -¼ m = vertical horizontal Note:Always draw the horizontal before the vertical: horizontal (+ve) vertical (-ve)

19. (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? STATISTICS : Question 3 Full solution Comments Statistics Menu Reveal EXIT Get hint 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 Simpsons Like Shrek Don’t like Simpsons Don’t like Shrek 126 2115 ?

20. (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? STATISTICS : Question 3 Full solution Comments Statistics Menu Reveal EXIT 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 Simpsons Like Shrek Don’t like Simpsons Don’t like Shrek 126 2115 ? Remember all entries in table must add to total sample size To find probabilities use: P = no of favourable / no of data What would you like to do now?

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? STATISTICS : Question 3 Full solution Comments Statistics Menu EXIT 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 Simpsons Like Shrek Don’t like Simpsons Don’t like Shrek 126 2115 ? 10% 1 / 12 7 / 60 What now?

22. Comments Begin Solution Continue Solution Question 3 Statistics Menu Back to Home 1. Use P = no of favourable / no of data Like Simpsons Like Shrek Don’t like Simpsons Don’t like Shrek 126 2115 ? (a)What percentage liked Shrek but not the Simpsons? (a) Like Shrek but not Simpsons = 180 – 126 – 15 – 21 = 18 % = 18 / 180 = 1 / 10 = 10% NB: There are 180 in survey!!

23. Comments Begin Solution Continue Solution Question 3 Statistics Menu Back to Home 1. Use P = no of favourable / no of data Like Simpsons Like Shrek Don’t like Simpsons Don’t like Shrek 126 2115 ? what is the probability that (i)they liked the Simpsons but not Shrek? (b)(i) Prob = 15 / 180 = 1 / 12

24. Comments Begin Solution Continue Solution Question 3 Statistics Menu Back to Home 1. Use P = no of favourable / no of data Like Simpsons Like Shrek Don’t like Simpsons Don’t like Shrek 126 2115 ? (ii) they liked neither? (b)(ii) Prob = 21 / 180 = 7 / 60 What would you like to do now?

25. Comments Statistics Menu Back to Home Next Comment 1. Use P = no of favourable / no of data (a) Like Shrek but not Simpsons = 180 – 126 – 15 – 21 = 18 % = 18 / 180 = 1 / 10 = 10% NB: There are 180 in survey!! Note: To change a fraction to a % multiply by 100% 18 180 = x 100% 18 180

26. Comments Statistics Menu Back to Home Next Comment 1. Use P = no of favourable / no of data (b)(i) Prob = 15 / 180 = 1 / 12 Probability = Number of favourable outcomes Number of possible outcomes To calculate simple probabilities:

27. (b)If a combination is selected at random what is the probability that it is …… STATISTICS : Question 4 Full solution Comments Stats Menu Reveal ans EXIT Get hint On a college course you have to pick a language plus a leisure activity from the following lists LANGUAGE FRENCH GERMAN SPANISH LEISURE MUSIC VIDEO PRODUCTION BASKETBALL SWIMMING (a) Make a list of all possible combinations of courses. (i) Includes Spanish? (ii) Includes swimming? (iii) Doesn’t include French but includes music?

28. (b)If a combination is selected at random what is the probability that it is …… STATISTICS : Question 4 Full solution Comments Stats Menu Reveal ans EXIT On a college course you have to pick a language plus a leisure activity from the following lists LANGUAGE FRENCH GERMAN SPANISH LEISURE MUSIC VIDEO PRODUCTION BASKETBALL SWIMMING (a) Make a list of all possible combinations of courses. (i) Includes Spanish? (ii) Includes swimming? (iii) Doesn’t include French but includes music? Use a tree diagram & “branch out” with each language. From each language “branch out” with each leisure activity. Now list the pairs of subjects. Use your list of possible combinations to find probabilities. What would you like to do now?

29. (b)If a combination is selected at random what is the probability that it is …… STATISTICS : Question 4 Full solution Comments Stats Menu EXIT On a college course you have to pick a language plus a leisure activity from the following lists LANGUAGE FRENCH GERMAN SPANISH LEISURE MUSIC VIDEO PRODUCTION BASKETBALL SWIMMING (a) Make a list of all possible combinations of courses. (i) Includes Spanish? (ii) Includes swimming? (iii) Doesn’t include French but includes music? 1/31/3 1/41/4 1/61/6 CLICK

30. GERMAN FRENCH SPANISH BASKETBALL VIDEO MUSIC SWIMMING BASKETBALL VIDEO MUSIC SWIMMING BASKETBALL VIDEO MUSIC SWIMMING (a) French/Music French/Video French/Bsktbll French/Swim German/Music 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.

31. Hints Have list of combinations handy. Remember to simplify. French/Music French/Video French/Bsktbll French/Swim German/Music German/Video German/Bsktbll German/Swim Spanish/Music Spanish/Video Spanish/Bsktbll Spanish/Swim = 1 / 3 = 1 / 4 (b)(i) Prob (b)(ii) Prob = 4 / 12 = 3 / 12 (b)(iii) Prob = 2 / 12 = 1 / 6 Comments Stats Menu What now? (i) Includes Spanish? (ii) Includes swimming? (iii)Doesn’t include French but includes music? What is probability:

32. Comments Statistics Menu Back to Home Next Comment GERMAN FRENCH SPANISH BASKETBALL VIDEO MUSIC SWIMMING BASKETBALL VIDEO MUSIC SWIMMING BASKETBALL VIDEO MUSIC SWIMMING (a) French/Music French/Video French/Bsktbll French/Swim German/Music German/Video German/Bsktbll German/Swim Spanish/Music Spanish/Video Spanish/Bsktbll Spanish/Swim No. of possible outcomes = 3 x 4 = 12 Probability = Number of favourable Number of possible To calculate simple probabilities:

33. The delivery times for a fast food company are shown in the following cumulative frequency table. Time No. Deliveries up to 4 mins 5 up to 8 mins 13 up to 12 mins 37 up to 16 mins 53 up to 20 mins 60 (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. (a)How many deliveries took longer than 16 mins? STATISTICS : Question 5 Full solution Comments Stats Menu Reveal ans Get hint

34. The delivery times for a fast food company are shown in the following cumulative frequency table. Time No. Deliveries up to 4 mins 5 up to 8 mins 13 up to 12 mins 37 up to 16 mins 53 up to 20 mins 60 (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. (a)How many deliveries took longer than 16 mins? STATISTICS : Question 5 Full solution Comments Stats Menu Reveal ans For how many greater than 16 find difference between end value of values up to 16. Median is middle value- so we want halfway- point on frequency axis. SIQR = ½(Q3 – Q1) Q1 – 25% point & Q3 – 75% point What would you like to do now?

35. The delivery times for a fast food company are shown in the following cumulative frequency table. Time No. Deliveries up to 4 mins 5 up to 8 mins 13 up to 12 mins 37 up to 16 mins 53 up to 20 mins 60 (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. (a)How many deliveries took longer than 16 mins? STATISTICS : Question 5 Full solution Comments Stats Menu = 7 Median = 11 minsSIQR = 2.75 mins

36. Delivery time(mins) Cum freq Q2 11 Q1 8.5 Q3 14 ½ of 60 = 30 ¼ of 60 = 15 ¾ of 60 = 45 (C) Median = 11mins. (c) SIQR = ½(Q3 – Q1) = (14 – 8.5)  2 = 2.75mins (a) Deliveries taking longer than 16 mins = 60 – 53= 7 Comments Stats Menu TimeDeliveries 45 813 1237 1653 2060 What would you like to do now?

37. Comments Statistics Menu Back to Home Next Comment Cumulative Frequency Delivery Time 60 20 50% 11 Note: In a Cumulative Frequency Diagram: On y-axis (cumulative frequency) Q 1 at 25%, Q 2 at 50%, Q 3 at 75% And read values from the delivery time scale (x-axis). End of Statistics