Research Design in Occupational Education


MODULE S1 DESCRIPTIVE STATISTICS All educators are involved in research and statistics to a degree. For this reason all educators should have a practical understanding of research design. Even if an educator is not involved in conducting research, he or she must be involved in the interpretation of the findings of others to remain dynamic in their teaching. The primary use of descriptive statistics is to describe information or data through the use of numbers (create number pictures of the information). The characteristics of groups of numbers representing information or data are called descriptive statistics. Descriptive statistics are used to describe groups of numerical data such as test scores, number or hours of instruction, or the number of students enrolled in a particular course.
The use of symbols is a convenient way of expressing parameters or statistics in research work. The following symbols are generally used to express parameters and statistics.
Note that for the mean, variance, and standard deviation lower case Greek letters are used to symbolize parameters, while lower case Roman letters are used to symbolize statistics. In the examples given, the raw scores for the 10 pt. quiz are: 10 9 8 8 7 7 6 6 5 4 2 10 9 8 8 7 6 6 5 5 3 10 9 8 7 7 6 6 5 4 3
Calculating Parameters and Statistics Suppose ten students made the following scores on a five point quiz. Calculate the measures of central tendency and variation.
*Note: n  1 used for small samples (usually less than 30 numbers).
Measures of Central Tendency Mode = Number which occurs most often Median = Middle number  50% above  50% below Mean = Average = M = =
Measures of Variation Range = Distance from highest to lowest score Variance = Squared standard deviation = s^{2} = Standard deviation = average distance of individual numbers from the mean 
Normal Curve
Percentages Percentages are used to relate how much a part is of the whole and established a basis for comparing information from groups of unequal sizes. Example

Group A had 36 (50%) students who agreed with the statement while Group B had 25 (75%) students who agreed. 
1. The primary use of descriptive statistics is to _____________________
2. Define:
a. Descriptive Statistics
b. Variable
c. Population
d. Parameter
e. Sample
f. Statistic
g. Mean
h. Median
i. Mode
j. Range
k. Variance
3. The frequency graph, bar graph or histogram, frequency polygon, and frequency curve are all means of _____________________illustrating data.
4. Label the following symbol as either a parameter or statistic.
Symbol Parameter Statistic
5. Identify by correctly labeling the following graphic illustrations of results of a five point quiz taken by ten students.
a._____________________ b. _____________________
c._____________________ d. _____________________
6. Construct a frequency graph, a histogram, a frequency polygon and a frequency curve to graphically illustrate the following data.
Scores on a ten point quiz taken by fifteen students:
Student Score Student Score Student Score
A 5 F 10 K 8
B 7 G 6 L 6
C 8 H 7 M 8
D 7 I 8 N 8
E 9 J 9 O 9
7. Calculate the measures of central tendency (mean, median and mode) and the measures of variation (range, variance and standard deviation) for the following scores.
x
5
6
7
7
7
8
8
8
8
8
9
9
10
10
10
= Mode =
n = Median =
= Range =
Variance =
Standard Deviation =
8. Out of a normally distributed population, what percentage of the population falls within two standard deviations of the mean?
9. Out of 200 students, 150 agreed with the statement. What percentage of the students agreed?