HED 241 BIOSTATISTICS IN PUBLIC HEALTH: STANDARD DEVIATION PART B:11

10) Suppose M=30 and S=3 for normal distribution of scores. What percentage of the cases lies between scores of 27 and 30?

Example: M=30 and S= 3 where 34% of the cases lie between scores of 27 and 30, (p. 51).

3) The standard deviation provides an overall measurement of how much participants' scores differ from what other statistic?

The standard deviation provides an overall measurement of how much participants' scores differ from the MEAN score of their group, (49).

1) The term variability refers to what?

Variability (spread or dispersion) refers to the differences of scores among participants, (45,49)

standard distribution

normal distribution w/ mean = 0 and S = 1 used for most calculations Standard deviation is within one standard unit from the Mean.

19. Interquartile range

(think about % in the book) REMEMBER THE 68% RULE GOES WITH THE INTERQUARTILE RANGE. 25% [25+25] 25% Quartiles divide a rank-ordered data set into four equal parts. 333 444 566 778 lower 25 % are 333 higher 25% are 778 middle 50% is 444 566 6-4=2 IQR = 2.

computation of standard deviation

159 standard deviation is the square root of the average squared deviation from the mean.

Mean: recap how to calculate

37 sum of all scores divided by the number of the scores = M

21. Standard deviation score

50 2/3 of cases 68% lie within one standard deviation unit of the MEAN in a normal distribution. example: M=70 S= 10 this states that 68% of the cases lie in the middle area in this case it is within 10 points of the Mean. 34% lie between 60-70 34% lie between 70-80 68% lie between 60-80

9) What percentage of the cases in a normal curve lies within one standard deviation unit of the mean (i.e. within one unit above and one unit below the mean)?

About two-thirds of cases or 68% lie within one standard deviation unit of the mean in a normal distribution, (50).

4) If the differences among a set of scores are small this indicates which of the following? A. there is much variability. B. there is little variability.

B. there is little variability.

when all scores are the same what is the standard deviation?

S=0.00 example: if all scores are 20 the Mean score is 20 there is no standard deviation so it is S=0.00 standard deviation equals 0.00.

11) Suppose M=80 and S= 10 for a normal distribution of scores. About 68% of the bases lie between what two scores?

Example: M=80 and S=10 in normal distribution of scores where 68% of cases lie between 70 and 90, (p. 51).

6) Will the scores for "Group D" or Group E" below have a larger standard deviation if the two standard deviations are computed? (do not compute the standard deviations; examine the scores to determine the answer) Group D: 23,23,24,25,27,27,27 Group E: 10,19,20,21,25,30,40

Group E would have a larger standard deviation due to scores going from 10 to 40 whereas in group D the scores are from 23 to 27.

8) If you read the following statistics in a research report, which group should you conclude has the greatest variability? Group F: M=30.23, S=2.14 Group G: M= 25.99, S=3.01 Group H: M=22.43, S=4.79

Group H has the greatest variability demonstrating a standard variation of 4.79 higher than group F with a standard variation of 2.14 and group G with a standard variation of 3.01, (p. 53).

7) If all the participants in a group have the same score, what is the value of the standard deviation of the scores?

If all participants have the same score there is no variability in the group's scores therefor the standard deviation equals zero (S = 0.00), (49)

22. Normal distribution/standard deviation how do the two work together.

Standard deviation was designed to describe the normal curve;Standard deviation is within one standard unit from the Mean.Basic rule is 2/3 (68%) of cases lie within one standard deviation unit of the mean in a normal distribution. (50). See figure 11.2 page 51

5) What is the symbol for the standard deviation when a population has been studied?

The upper case italicized S , (49).

2) Is the standard deviation a frequently used measure of variability?

YES, The standard deviation is the MOST FREQUENTLY USED measure of variability, (49)

20. Standard deviation (know how to identify the standard deviation score)

if she tells you the mean is 30 and the standard deviation is 10 what does that mean? Standard deviation shows how your score differs from the mean score; M30+S10=40 M30-S10=20, 68% of the population scores range from 20 to 40 when it is a normal curve and the standard deviation is 30. OR say 34% score between 30-40 34% score between 20-30. The farther out from the mean the larger the standard deviation is. (Ppt B11 p 2) HOW TO CALCULATE: APPENDIX A (159)

*****sample statement reporting M & S

ppt B 11 last page Group A ( M=67.89, S=8.77) has higher Mean. Group B (M=60.23, S=8.54) Group A has a higher Mean with average of 67.89 with a Standard deviation of 8.77 than group B which had a Mean of 60.23 in a Standard deviation of 8.54.