interpreting performance data

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Interpreting Performance Data. Expected Outcomes . Understand the terms mean, median, mode, standard deviation Use these terms to interpret performance data supplied by EAU. Measures of Central Tendency . Mean … the average score - PowerPoint PPT Presentation

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• Interpreting Performance Data

• Expected Outcomes Understand the terms mean, median, mode, standard deviation

Use these terms to interpret performance data supplied by EAU

• Measures of Central Tendency Mean the average score

Median the value that lies in the middle after ranking all the scores

Mode the most frequently occurring score

• Which measure of Central Tendency should be used?

Measures of Central Tendency

• Measures of Central Tendency The measure you choose should give you a good indication of the typical score in the sample or population.

• Measures of Central Tendency Mean the most frequently used but is sensitive to extreme scorese.g. 1 2 3 4 5 6 7 8 9 10Mean = 5.5 (median = 5.5)e.g. 1 2 3 4 5 6 7 8 9 20Mean = 6.5 (median = 5.5)e.g. 1 2 3 4 5 6 7 8 9 100Mean = 14.5 (median = 5.5)

• Measures of Central Tendency Median

is not sensitive to extreme scores

use it when you are unable to use the mean because of extreme scores

• Measures of Central Tendency Mode

does not involve any calculation or ordering of data

use it when you have categories (e.g. occupation)

• A Distribution CurveMean: 54Median: 56Mode: 63

• The Normal Distribution Curve In everyday life many variables such as height, weight, shoe size and exam marks all tend to be normally distributed, that is, they all tend to look like the following curve.

• The Normal Distribution CurveIt is bell-shaped and symmetrical about the meanThe mean, median and mode are equalMean, Median, ModeIt is a function of the mean and the standard deviation

Chart1

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0.00416119960

0.00371509180

0.00330489070

0.00292941690

0.00258727040

0.00227687390

0.00199651550

0.00174438730

0.00151862210

0.00131732530

0.00113860450

0.00098059420

0.0008414770

0.00071950160

0.00061299620

0.00052037970

0.0004401690

0.00037098390

0.00031154960

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WELCOME SCREEN

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Welcome to DISCUS 5 !

Workbook for Continuous Distributions

copyright Neville Hunt & Sidney Tyrrell 1995

INTRODUCTION

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DISCUS 5 is a workbook about continuous distributions.

It is designed to help you understand more about : the Normal distribution the Exponential distribution the Student's t distribution the Beta distribution the Chi-squared distribution the Gamma distribution the F distribution the Weibull distribution and to show comparisons between them.

Self-teaching notes and questions are provided for each topic on separate workcards which are designed to be USED with the workbook.

There is a spare spreadsheet at the end of the workbook which can be used in the usual way for making notes, recording results, or doing calculations.

NORMAL DISTRIBUTION HELP SCREEN

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Aim: To see how the Normal distribution alters with different means and standard deviations.

Three plots are given. Change the means and standard deviations, highlighted in blue, to compare different normal distributions.

DISCUS 5.1

NORMAL DISTRIBUTION

Plot 1Plot 2Plot 3

Mean5000

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1.040.000370983900

2.060.00044016900

3.080.000520379700

4.10.000612996200

5.120.000719501600

6.140.00084147700

7.160.000980594200

8.180.001138604500

9.20.001317325300

10.220.001518622100

11.240.001744387300

12.260.001996515500

13.280.002276873900

14.30.002587270400

15.320.002929416900

16.340.003304890700

17.360.003715091800

18.380.004161199600

19.40.00464412700

20.420.005164474700

21.440.005722486400

22.460.006318004400

23.480.006950429100

24.50.007618682100

25.520.008321174400

26.540.009055781600

27.560.00981982600

28.580.010610068400

29.60.011422709100

30.620.012253399400

31.640.013097264600

32.660.013948938400

33.680.014802608300

34.70.015652073500

35.720.016490812400

36.740.017312060600

37.760.018108897700

38.780.018874341400

39.80.019601447200

40.820.020283411800

41.840.020913678100

42.860.021486039600

43.880.021994741500

44.90.022434577400

45.920.022800977400

46.940.023090087200

47.960.02329883600

48.980.0234249900

500.02346719300

51.020.0234249900

52.040.02329883600

53.060.023090087200

54.080.022800977400

55.10.022434577400

56.120.021994741500

57.140.021486039600

58.160.020913678100

59.180.020283411800

60.20.019601447200

61.220.018874341400

62.240.018108897700

63.260.017312060600

64.280.016490812400

65.30.015652073500

66.320.014802608300

67.340.013948938400

68.360.013097264600

69.380.012253399400

70.40.011422709100

71.420.010610068400

72.440.00981982600

73.460.009055781600

74.480.008321174400

75.50.007618682100

76.520.006950429100

77.540.006318004400

78.560.005722486400

79.580.005164474700

80.60.00464412700

81.620.004161199600

82.640.003715091800

83.660.003304890700

84.680.002929416900

85.70.002587270400

86.720.002276873900

87.740.001996515500

88.760.001744387300

89.780.001518622100

90.80.001317325300

91.820.001138604500

92.840.000980594200

93.860.00084147700

94.880.000719501600

95.90.000612996200

96.920.000520379700

97.940.00044016900

98.960.000370983900

99.980.000311549600

1010.00026069700

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5.1 The Normal distribution

NORMAL DISTRIBUTION

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t DISTRIBUTION HELP SCREEN

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USING the Student's t Distribution spreadsheet

Aim: To see how the shape of the Student's t distribution changes as the number of degrees of freedom is altered.

Three plots are given. Change the values of the degrees of freedom, highlighted in blue, to compare different t distributions.

DISCUS 5.2

STUDENT'S t DISTRIBUTION

Plot 1Plot 2Plot 3

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