1. Whiteboardmaths.com © 2007 All rights reserved 5 7 2 1

2. Notes for Teachers The presentation starts by taking a look at the more intuitive idea of mean deviation before leading on to standard deviation. Although the example is based on sampled data, x  n is used rather than x  n – 1. Use of a scientific calculator to calculate mean and standard deviation is placed in a single area (sides 28 to 37). The first 4 slides look at the key sequences for single data entry for each of: 1. Casio fx-83MS, 2. Casio fx-83ES (natural display), 3. Sharp EL-531H 4. TEXET (ALB  RT). The same example question is used on each of the calculators. This is followed by 2 student questions on slide 32. A similar structure occurs on the next 5 slides for data displayed in frequency table form. Clearly you are going to have to dip in and out of this area to find what suits. If you want print-outs of the calculator key sequences they have been included at the back of the presentation (slides 53 – 60) We then move on to look at “comparing data” and “related data”. There are worksheets at the back. As with many of these presentations you may not want to run the slides in the exact sequence given, so you need look around to find what suits.

3. Intro Standard Deviation In summarising a set of data we often give a measure of average and a measure of spread. Three measures of average so far used are the: These are known as measures of central tendency and enable us to locate the centre of distribution for a set of data. mean, mode and median Two measures of spread that we have previously used are the: range, and inter-quartile range These are known as measures of dispersion and they give us a measure of how spread-out (dispersed) the data is about the mean and median respectively. 456789101112 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Median = 8 IQR = 4.5 Mean  7.7 Range = 8

4. Standard Deviation In summarising a set of data we often give a measure of average and a measure of spread. Three measures of average so far used are the: These are known as measures of central tendency and enable us to locate the centre of distribution for a set of data. mean, mode and median Two measures of spread that we have previously used are the: range, and inter-quartile range 456789101112 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Median = 8 IQR = 4.5 Mean  7.7 Range = 8 A third measure of dispersion is called Standard Deviation. This is an important and much more accurate way to measure dispersion about the mean.

5. Standard Deviation We will introduce the idea standard deviation by first considering the table below. This table is a sample of the marks from five students that sat the same test in three different classes. ClassMean ( x )Range A80 40 6440 B80766856406440 C6564 63642 Each class had a mean mark of 64 but the spread/dispersion/variation of marks show large differences. Sample Marks Scored in Test The range gives a poor measure of variation in this example. Classes A and B have the same range but none of the marks in class A are close to the mean, whereas some of the marks in class B are. In class C all of the marks are close to the mean. It is this concept of “Closeness to the mean” that leads to the definition of standard deviation.

6. Standard Deviation We could calculate “Closeness to the mean” for each class by considering the average of differences between the student marks and the mean mark as follows: ClassMean ( x )Range A80 40 6440 B80766856406440 C6564 63642 Sample Marks Scored in Test Class Ax - x 80 40 Class Bx - x 80 76 68 56 40 Class Cx - x 65 64 63 Can you spot the problem with taking this approach?

7. Standard Deviation We could calculate “Closeness to the mean” for each class by considering the average of differences between the student marks and the mean mark as follows: ClassMean ( x )Range A80 40 6440 B80766856406440 C6564 63642 Sample Marks Scored in Test Class Ax - x 8016 8016 8016 40-24 40-24 Class Bx - x 8016 7612 684 56-8 40-24 Class Cx - x 651 640 0 0 63 Can you spot the problem with taking this approach?

8. Standard Deviation ClassMean ( x )Range A80 40 6440 B80766856406440 C6564 63642 Sample Marks Scored in Test Class Ax - x 8016 8016 8016 40-24 40-24 Class Bx - x 8016 7612 684 56-8 40-24 Class Cx - x 651 640 0 0 63 In each case so

9. Mean Deviation Standard Deviation Class Ax - x 8016 8016 8016 4024 4024 Class Bx - x 8016 7612 684 568 4024 Class Cx - x 651 640 0 0 631 It is better to consider the “Closeness to the mean” by considering the average distance (not difference) between the student marks and the mean mark. This approach allows us to ignore the negative sign in each case and complete the calculation of the Mean Deviation as follows: 96 64 2

10. Standard Deviation Class Ax - x 8016 8016 8016 4024 4024 Class Bx - x 8016 7612 684 568 4024 Class Cx - x 651 640 0 0 631 Whist the mean deviation is a natural and intuitive measure of dispersion the method employed in eliminating the minus signs makes analytical calculations in more advanced statistics far more complex. This measure is therefore not used. 96 64 2 However, with only a slight modification and a different method of eliminating the minus sign we can define standard deviation.

11. Standard Deviation We calculate the standard deviation by squaring all the entries in the deviations column to eliminate the minus signs. We then find the mean of the sum of this column (Variance) before finally taking the square root to arrive at the standard deviation. Variance = Class Ax - x(x - x) 2 8016 8016 8016 40-24 40-24 Class Bx - x(x - x) 2 8016 7612 684 56-8 40-24 Class Bx - x(x - x) 2 651 640 0 0 63

12. Standard Deviation We calculate the standard deviation by squaring all the entries in the deviations column to eliminate the minus signs. We then find the mean of the sum of this column (Variance) before finally taking the square root to arrive at the standard deviation. Variance = Class Ax - x(x - x) 2 8016256 8016256 8016256 40-24576 40-24576 Class Bx - x(x - x) 2 8016256 7612144 68416 56-864 40-24576 Class Bx - x(x - x) 2 6511 6400 00 00 631

13. Standard Deviation We calculate the standard deviation by squaring all the entries in the deviations column to eliminate the minus signs. We then find the mean of the sum of this column (Variance) before finally taking the square root to arrive at the standard deviation. Variance = Class Ax - x(x - x) 2 8016256 8016256 8016256 40-24576 40-24576 Class Bx - x(x - x) 2 8016256 7612144 68416 56-864 40-24576 Class Bx - x(x - x) 2 6511 6400 00 00 631 1920 1056 2

14. Standard Deviation ClassMean ( x )Range A80 40 6440 B80766856406440 C6564 63642 Sample Marks Scored in Test We can see how much better a measure of dispersion the standard deviation is by looking back at the original table where class A and B had the same range. Class A Class B Class C No marks close to mean Some marks close to mean All marks close to mean The higher the standard deviation, the greater the dispersion or spread of data. The lower the standard deviation the less dispersion or variability of data.

15. EXQ1 Standard Deviation Example Question 1 Calculate the mean and standard deviation of 3, 4, 5, 6, 7, 8, 9. Mean = 42/7 = 6 xx - x(x – x) 2 3 4 5 6 7 8 9

16. Standard Deviation Example Question 1 Calculate the mean and standard deviation of 3, 4, 5, 6, 7, 8, 9. Mean = 42/7 = 6 xx - x(x – x) 2 3-3 4-2 5 60 71 82 93

17. Standard Deviation Example Question 1 Calculate the mean and standard deviation of 3, 4, 5, 6, 7, 8, 9. Mean = 42/7 = 6 xx - x(x – x) 2 3-39 4-24 51 600 711 824 939 28

18. Q1 Standard Deviation Question 1 Calculate the mean and standard deviation of 8, 9, 10, 11, 12. Mean = 50/5 = 10 xx - x(x – x) 2 8 9 10 11 12

19. Standard Deviation Question 1 Calculate the mean and standard deviation of 8, 9, 10, 11, 12. Mean = 50/5 = 10 xx - x(x – x) 2 8-2 9 100 111 122

20. Standard Deviation Question 1 Calculate the mean and standard deviation of 8, 9, 10, 11, 12. Mean = 50/5 = 10 xx - x(x – x) 2 8-24 91 1000 1111 1224 10

21. EXQ2 Standard Deviation Example Question 2 Calculate the mean and standard deviation of : 6, 7.3, 9, 6.4, 8, 5.3 Mean = 42/6 = 7 xx - x(x – x) 2 6 7.3 9 6.4 8 5.3

22. Standard Deviation Example Question 2 Calculate the mean and standard deviation of : 6, 7.3, 9, 6.4, 8, 5.3 Mean = 42/6 = 7 xx - x(x – x) 2 6- 1 7.30.3 92 6.4- 0.6 81 5.3- 1.7

23. Standard Deviation Example Question 2 Calculate the mean and standard deviation of : 6, 7.3, 9, 6.4, 8, 5.3 Mean = 42/6 = 7 xx - x(x – x) 2 6- 11 7.30.30.09 924 6.4- 0.60.36 811 5.3- 1.72.89 9.34

24. Q2 Standard Deviation Question 2 Calculate the mean and standard deviation of : 1.7, 6.7, 5.9, 8.1, 8, 3.1, 10.3, 7.4 Mean =51.2 /8 = 6.4 xx - x(x – x) 2 1.7 6.7 5.9 8.1 8 3.1 10.3 7.4

25. Standard Deviation Question 2 Calculate the mean and standard deviation of : 1.7, 6.7, 5.9, 8.1, 8, 3.1, 10.3, 7.4 Mean =51.2 /8 = 6.4 xx - x(x – x) 2 1.7- 4.7 6.70.3 5.9- 0.5 8.11.7 81.6 3.1- 3.3 10.33.9 7.41

26. Standard Deviation Question 2 Calculate the mean and standard deviation of : 1.7, 6.7, 5.9, 8.1, 8, 3.1, 10.3, 7.4 Mean =51.2 /8 = 6.4 xx - x(x – x) 2 1.7- 4.722.09 6.70.30.09 5.9- 0.50.25 8.11.72.89 81.62.56 3.1- 3.310.89 10.33.915.21 7.411 54.98

27. Other Formulae Standard Deviation Calculate the standard deviation of 3, 4, 5, 6, 7, 8, 9 xx2x2 39 416 525 636 749 864 981 x = 42/7 = 6 280 There are other ways of writing the formula for standard deviation that can sometimes make the calculation easier. Examples of two of these formulae and how they are applied are demonstrated on an earlier question. You may want to try these formulae out on earlier questions.

28. SCI Calc (CASIO fx83MS) Standard Deviation Using a Scientific Calculator to calculate Standard Deviation Scientific calculators can be used to calculate the mean and standard deviation of any set of data once all the data values have been entered. Calculate the mean and standard deviation of: 3, 4, 5, 6, 7, 8, 9.Ex Q 1 We did this question earlier and found that the mean = 6 and SD = 2. We will now do this calculation on a CASIO calculator. Casio f x -83MS The following key sequence is used to enter the data (data button DT below M+). M+3 4 5 6 7 8 9 For SD (x  n) press: Shift22= Display shows 2 ShiftCLR3AC Clear stat memory by pressing Select stat mode by pressing Mode2 For the mean x press: Shift21= Display shows 6

29. SCI Calc (CASIO fx83ES) Standard Deviation Using a Scientific Calculator to calculate Standard Deviation Scientific calculators can be used to calculate the mean and standard deviation of any set of data once all the data values have been entered. We did this question earlier and found that the mean = 6 and SD = 2. We will now do this calculation on a CASIO calculator. Casio f x -83ES Mode21 To enter single variable stat data press Shift93= Clear stat memory by pressing AC Enter the data using the following key sequence: 3=4=5=6=7=8=9=ACShift153 To show SD (x  n ) press: = Displays 2 Shift152 To show the mean x press: = Displays 6 Calculate the mean and standard deviation of: 3, 4, 5, 6, 7, 8, 9.Ex Q 1

30. Sharp CALC Standard Deviation Using a Scientific Calculator to calculate Standard Deviation Scientific calculators can be used to calculate the mean and standard deviation of any set of data once all the data values have been entered. Sharp: EL-531VH The DATA button is below the M+ key so the following key sequence is used to enter the data. M+3 4 5 6 7 8 9 For SD (  x) press: RCL6 Display shows 2 We did this question earlier and found that the mean = 6 and SD = 2. We will now do this calculation on a SHARP calculator. Calculate the mean and standard deviation of: 3, 4, 5, 6, 7, 8, 9.Ex Q 1 For the Mean x press: RCL4 Display shows 6 Clear the stat memories by pressing:2ndFCA Enter stat mode by pressing: 2ndFMode1

31. TEXET CALC Standard Deviation Using a Scientific Calculator to calculate Standard Deviation Scientific calculators can be used to calculate the mean and standard deviation of any set of data once all the data values have been entered. Calculate the mean and standard deviation of: 3, 4, 5, 6, 7, 8, 9.Ex Q 1 We did this question earlier and found that the mean = 6 and SD = 2. We will now do this calculation on a TEXET calculator. TEXET (ALB  RT) 3 The following key sequence is used to enter the data (data button DT below M+) M+3 4 5 6 7 8 9 For SD (x  n) press: Shift2= Display shows 2 ShiftScl= Clear stat memory by pressing Select stat mode by pressing Mode2 For the mean x press: Shift1= Display shows 6

32. (Q 1) Calculate the mean and standard deviation to (1 dp) of: 6, 7.3, 9, 6.4, 8, 5.3 (Q2) Calculate the mean and standard deviation (to 1 dp) of: 1.7, 6.7, 5.9, 8.1, 8, 3.1, 10.3, 7.4 Standard Deviation Using a Scientific Calculator to calculate Standard Deviation Mean = 7, standard deviation = 1.2 Mean = 6.4, standard deviation = 2.6

33. Frequency table 1 Standard Deviation Using a Scientific Calculator to calculate Standard Deviation Ex Q2 (Frequency Table) x238112025 f524326 Casio f x -83MS The following key sequence is used to enter the data (DT). For SD (x  n) press: Shift22= Displays 9.2 (1 dp) M+2SHIFT ; 5M+3SHIFT ; 2M+8SHIFT ; 4M+11SHIFT ; 3M+20SHIFT ; 2M+25SHIFT ; 6 Find the mean and standard deviation for the data shown in the table below. ShiftCLR3AC Clear stat memory by pressing Select stat mode by pressing Mode2 For the Mean x press: SHIFT21= Displays 12.3 (1 dp)

34. Frequency table 2 Standard Deviation Using a Scientific Calculator to calculate Standard Deviation x238112025 f524326 Casio f x -83ES The following key sequences are used to enter the data. Find the mean and standard deviation for the data shown in the table below. ShiftSetup To display the frequency column in SETUP press 31Mode21 To enter single variable stat data press 2=3=8=11=20=25=Shift153 To show SD (x  n ) press: = Displays 9.2 (1 dp) Shift152 To show the mean x press: = Displays 12.3 (1 dp) 5=2=4=3=2=6=AC Use Replay arrows to position curser in frequency table opposite 1 st data point. Shift93= Clear stat memory by pressing AC Ex Q2 (Frequency Table)

35. Frequency Table 3 Standard Deviation Using a Scientific Calculator to calculate Standard Deviation x238112025 f524326 The following key sequence is used to enter the data (DATA) M+2STO5M+3STO2M+8STO4M+11STO3M+20STO2M+25STO6 Find the mean and standard deviation for the data shown in the table below. Sharp: EL-531VH Clear the stat memories by pressing:2ndFCA Enter stat mode by pressing: 2ndFMode1 For SD (  x) press: RCL6 Display shows 9.2 For the Mean x press: RCL4 Display shows 12.3 Ex Q2 (Frequency Table)

36. Frequency table 4 Standard Deviation Using a Scientific Calculator to calculate Standard Deviation x238112025 f524326 The following key sequence is used to enter the data (DT). For SD (x  n) press: SHIFT2= Displays 9.2 (1 dp) M+2SHIFT ; 5M+3SHIFT ; 2M+8SHIFT ; 4M+11SHIFT ; 3M+20SHIFT ; 2M+25SHIFT ; 6 Find the mean and standard deviation for the data shown in the table below. For the Mean x press: SHIFT1= Displays 12.3 (1 dp) TEXET (ALB  RT) 3 ShiftScl= Clear stat memory by pressing Select stat mode by pressing Mode2 Ex Q2 (Frequency Table)

37. Question 3 x121520243238 f68141094 Find the mean and standard deviation (1 dp) for the data shown in the table below. Question 4 x758121326 f2593611 Find the mean and standard deviation (1 dp) for the data shown in the table below. Standard Deviation Mean = 22.6, standard deviation = 7.7 Mean = 14.2, standard deviation = 8.2

38. Comparing Data Standard Deviation Comparing Data Paper 156436587544330716554 Paper 222835293637829948019 Ten students sat two maths papers and their results are recorded in the table below. Calculate the mean and standard deviation for both papers and comment on the results of the tests. Mean and standard deviation for paper 1 = 56.8 and 15.4 (1 dp) Mean and standard deviation for paper 2 = 61.3 and 27.6 (1 dp) Paper 1 was the more difficult paper as the mean score was lower than paper 2. Although the average mark was higher on paper 2 the spread of results was much more varied (higher standard deviation). Example Question 1

39. Q5 Standard Deviation Comparing Data Jan - Jun£96£72£65£80£120£131 July - Dec£152£178£84£23£92£29 Mike runs a small business and has a business telephone. He recorded the cost of calls for each half of the year. Calculate the mean and standard deviation of both sets of data and comment on the cost and distribution of bills for both periods. Mean and standard deviation for first half of year = £94 and £24.39 Mean and standard deviation for second half of year = £93 and £57.42 The average cost of calls are very similar for both periods although in the second period the cost of calls are much more varied (higher standard deviation). Question 1

40. Q6 Standard Deviation Comparing Data Sure Fit2028272419302825 Easy Fit2630192625271718 A car magazine publishes a report on car exhausts bought and tested from two different suppliers. A sample of eight exhausts is chosen from each and tested. The tests give an indication of average life expectancy (in months) of each exhaust. The results are shown in the table below. Calculate the mean and standard deviation of the life expectancy for both. Use your calculations to help recommend one of the suppliers to a friend. Mean and standard deviation for Sure Fit = 25.1 months and 3.7 months. Mean and standard deviation for Easy Fit = 23.5 months and 4.5 months. Sure Fit sell the better exhausts. They last on average 1.6 months longer than those of Easy Fit and their lower standard deviation also shows that they are more consistently reliable. Question 2

41. Related Data Standard Deviation Related Data Consider the data 3, 4, 5, 6, 7, 8, 9. The mean of this data is 6 and the standard deviation is 2. Calculate the mean and standard deviation of 8, 9, 10, 11, 12, 13, 14 Mean = 11 and standard deviation = 2. The mean has increased by 5 but the standard deviation is the same. 3 4 5 6 7 8 9 8 9 10 11 12 13 14 +5 Mean deviation (1 + 2 + 3)/3 = 2 A quick inspection of the mean deviations indicate that the standard deviations will remain unchanged. Generally if any set of data has all its values increased by a constant K then the resulting data will have a mean of “original mean + K” and the same SD.

42. Q7 Standard Deviation Related Data Question 1 (a) Calculate the mean and standard deviation of: 9, 6, 12, 11, 15 (b) Write down the mean of 20, 17, 23, 22, 26 (c) Write down the mean of 1, -2, 4, 3, 7 (a) Mean = 10.6 and SD = 3.0 (b) Mean = 21.6 and SD = 3.0 (c) Mean = 2.6 and SD = 3.0

43. Q8 Standard Deviation Related Data Question 2 (a) Calculate the mean and standard deviation of: 1, 2, 3, 4, 5 (b) Show that any set of 5 consecutive integers has the same standard deviation as in (a). (a) Standard deviation = (b) Any set of 5 consecutive integers can be obtained from the above set by adding a constant K. Therefore any five consecutive integers will have a SD of

44. Standard Deviation Related Data Consider the data 3, 4, 5, 6, 7, 8, 9. The mean of this data is 6 and the standard deviation is 2. Calculate the mean and standard deviation of 9, 12, 15, 18, 21, 24, 27 Mean = 18 and standard deviation = 6. Both the mean and standard deviation have tripled in value. 3 4 5 6 7 8 9 x3 9 12 15 18 21 24 27 Mean deviation (3 + 6 + 9)/3 = 6 A quick inspection of the mean deviations indicate that the standard deviations will triple in value. Generally if any set of data has all its values multiplied by a constant K then the mean and SD of the resulting data will be K times larger than the originals.

45. Q9 Standard Deviation Related Data Question 3 (a) Calculate the mean and standard deviation of: 2, 5, 11, 4, 9 (b) Write down the mean of 8, 20, 44, 16, 36 (c) Write down the mean of 0.5, 1.25, 2.75, 1, 2.25 (a) Mean = 6.2 and SD = 3.3 (1 dp) (b) Mean = 24.8 and SD = 13.2 (c) Mean = 1.55 and SD = 0.825

46. Worksheets Class Ax - x 80 40 Class Bx - x 80 76 68 56 40 Class Cx - x 65 64 63 Class Ax - x 80 40 Class Bx - x 80 76 68 56 40 Class Cx - x 65 64 63 Worksheet

47. Class Ax - x(x - x) 2 80 40 Class Bx - x(x - x) 2 80 76 68 56 40 Class Bx - x(x - x) 2 65 64 63 Class Ax - x(x - x) 2 80 40 Class Bx - x(x - x) 2 80 76 68 56 40 Class Bx - x(x - x) 2 65 64 63 Worksheet

48. Example Question 1 Calculate the mean and standard deviation of 3, 4, 5, 6, 7, 8, 9. Question 1 Calculate the mean and standard deviation of 8, 9, 10, 11, 12. Example Question 2 Calculate the mean and standard deviation of 6, 7.3, 9, 6.4, 8, 5.3 Question 2 Calculate the mean and standard deviation of : 1.7, 6.7, 5.9, 8.1, 8, 3.1, 10.3, 7.4 Worksheets (Slides 15 – 26)

49. Calculate the mean and standard deviation of: 3, 4, 5, 6, 7, 8, 9.Ex Q 1 (Q 1) Calculate the mean and standard deviation to (1 dp) of: 6, 7.3, 9, 6.4, 8, 5.3 (Q2) Calculate the mean and standard deviation (to 1 dp) of: 1.7, 6.7, 5.9, 8.1, 8, 3.1, 10.3, 7.4 Calculator Worksheets (slides 28 to 32)

50. Question 3 x121520243238 f68141094 Find the mean and standard deviation for the data shown in the table below. Worksheet from calculator section on frequency tables (slides 33 to 37) Question 4 x758121326 f2593611 Find the mean and standard deviation for the data shown in the table below. Example Question 2 x238112025 f524326 Find the mean and standard deviation for the data shown in the table below.

51. Paper 156436587544330716554 Paper 222835293637829948019 Ten students sat two maths papers and their results are recorded in the table below. Calculate the mean and standard deviation for both papers and comment on the results of the tests. Example Question 1 Jan - Jun£96£72£65£80£120£131 July - Dec£152£178£84£23£92£29 Mike runs a small business and has a business telephone. He recorded the cost of calls for each half of the year. Calculate the mean and standard deviation of both sets of data and comment on the cost and distribution of bills for both periods. Question 1 Sure Fit2028272419302825 Easy Fit2630192625271718 A car magazine publishes a report on car exhausts bought and tested from two different suppliers. A sample of eight exhausts is chosen from each and tested. The tests give an indication of average life expectancy (in months) of each exhaust. The results are shown in the table below. Calculate the mean and standard deviation of the life expectancy for both. Use your calculations to help recommend one of the suppliers to a friend. Question 2 Worksheet from Comparing data (Slides 37 = 39) Worksheets 5

52. Question 1 (a) Calculate the mean and standard deviation of: 9, 6, 12, 11, 15 (b) Write down the mean of 20, 17, 23, 22, 26 (c) Write down the mean of 1, -2, 4, 3, 7 Question 2 (a) Calculate the mean and standard deviation of: 1, 2, 3, 4, 5 (b) Show that any set of 5 consecutive integers has the same standard deviation as in (a). Question 3 (a) Calculate the mean and standard deviation of: 2, 5, 11, 4, 9 (b) Write down the mean of 8, 20, 44, 16, 36 (c) Write down the mean of 0.5, 1.25, 2.75, 1, 2.25 Worksheet from Related data (Slides 42 = 45)

53. Calculator Sequences Standard Deviation Using a Scientific Calculator to calculate Standard Deviation Scientific calculators can be used to calculate the mean and standard deviation of any set of data once all the data values have been entered. Calculate the mean and standard deviation of: 3, 4, 5, 6, 7, 8, 9.Ex Q 1 We did this question earlier and found that the mean = 6 and SD = 2. We will now do this calculation on a CASIO calculator. Casio f x -83MS The following key sequence is used to enter the data (data button DT below M+) M+3 4 5 6 7 8 9 For SD (x  n) press: Shift22= Display shows 2 ShiftCLR3AC Clear stat memory by pressing Select stat mode by pressing Mode2 For the mean x press: Shift21= Display shows 6

54. Standard Deviation Using a Scientific Calculator to calculate Standard Deviation Scientific calculators can be used to calculate the mean and standard deviation of any set of data once all the data values have been entered. We did this question earlier and found that the mean = 6 and SD = 2. We will now do this calculation on a CASIO calculator. Casio f x -83ES Mode21 To enter single variable stat data press Shift93= Clear stat memory by pressing AC Enter the data using the following key sequence: 3=4=5=6=7=8=9=ACShift153 To show SD (x  n ) press: = Displays 2 Shift152 To show the mean x press: = Displays 6 Calculate the mean and standard deviation of: 3, 4, 5, 6, 7, 8, 9.Ex Q 1

55. Standard Deviation Using a Scientific Calculator to calculate Standard Deviation Scientific calculators can be used to calculate the mean and standard deviation of any set of data once all the data values have been entered. Sharp: EL-531VH The DATA button is below the M+ key so the following key sequence is used to enter the data. M+3 4 5 6 7 8 9 For SD (  x) press: RCL6 Display shows 2 We did this question earlier and found that the mean = 6 and SD = 2. We will now do this calculation on a SHARP calculator. Calculate the mean and standard deviation of: 3, 4, 5, 6, 7, 8, 9.Ex Q 1 For the Mean x press: RCL4 Display shows 6 Clear the stat memories by pressing:2ndFCA Enter stat mode by pressing: 2ndFMode1

56. Standard Deviation Using a Scientific Calculator to calculate Standard Deviation Scientific calculators can be used to calculate the mean and standard deviation of any set of data once all the data values have been entered. Calculate the mean and standard deviation of: 3, 4, 5, 6, 7, 8, 9.Ex Q 1 We did this question earlier and found that the mean = 6 and SD = 2. We will now do this calculation on a TEXET calculator. TEXET (ALB  RT) 3 The following key sequence is used to enter the data (data button DT below M+) M+3 4 5 6 7 8 9 For SD (x  n) press: Shift2= Display shows 2 ShiftScl= Clear stat memory by pressing Select stat mode by pressing Mode2 For the mean x press: Shift1= Display shows 6

57. Standard Deviation Using a Scientific Calculator to calculate Standard Deviation From a given frequency table x238112025 f524326 Casio f x -83MS The following key sequence is used to enter the data (DT). For SD (x  n) press: Shift22= Displays 9.2 (1 dp) M+2SHIFT ; 5M+3SHIFT ; 2M+8SHIFT ; 4M+11SHIFT ; 3M+20SHIFT ; 2M+25SHIFT ; 6 Find the mean and standard deviation for the data shown in the table below. ShiftCLR3AC Clear stat memory by pressing Select stat mode by pressing Mode2 For the Mean x press: SHIFT21= Displays 12.3 (1 dp)

58. Standard Deviation Using a Scientific Calculator to calculate Standard Deviation From a given frequency table x238112025 f524326 Casio f x -83ES The following key sequences are used to enter the data. Find the mean and standard deviation for the data shown in the table below. ShiftSetup To display the frequency column in SETUP press 31Mode21 To enter single variable stat data press 2=3=8=11=20=25=Shift153 To show SD (x  n ) press: = Displays 9.2 (1 dp) Shift152 To show the mean x press: = Displays 12.3 (1 dp) 5=2=4=3=2=6=AC Use Replay arrows to position curser in frequency table opposite 1 st data point. Shift93= Clear stat memory by pressing AC

59. Standard Deviation Using a Scientific Calculator to calculate Standard Deviation From a given frequency table x238112025 f524326 The following key sequence is used to enter the data (DATA) M+2STO5M+3STO2M+8STO4M+11STO3M+20STO2M+25STO6 Find the mean and standard deviation for the data shown in the table below. Sharp: EL-531VH Clear the stat memories by pressing:2ndFCA Enter stat mode by pressing: 2ndFMode1 For SD (  x) press: RCL6 Display shows 9.2 For the Mean x press: RCL4 Display shows 12.3

60. Standard Deviation Using a Scientific Calculator to calculate Standard Deviation From a given frequency table x238112025 f524326 The following key sequence is used to enter the data (DT). For SD (x  n) press: SHIFT2= Displays 9.2 (1 dp) M+2SHIFT ; 5M+3SHIFT ; 2M+8SHIFT ; 4M+11SHIFT ; 3M+20SHIFT ; 2M+25SHIFT ; 6 Find the mean and standard deviation for the data shown in the table below. For the Mean x press: SHIFT1= Displays 12.3 (1 dp) TEXET (ALB  RT) 3 ShiftScl= Clear stat memory by pressing Select stat mode by pressing Mode2