The UON conducts both face to face (FF) and online (OL) classes that are intended to be identical. Given below are the distributions of the two groups in terms of marks scored in a statistics examination. The modal mark is known for each group and given as 68 for face to face and 64 for online students respectively. Marks 30- 40 40- 50 50- 60 60- 70 70- 80 80 – 90 90-100 Total F.F Students 6 18 12 f1 18 f2 12 100 O.N Students 5 15 f1 22 19 11 f2 100 a. Find the missing frequencies f1 and f2 for each. b. Based on the mean mark justify who should be rewarded for good performance. c. Based on Pearson’s second coefficient of skewness, compare and comment on skewness of the two groups, explaining what this implies with reference to the performance of each group
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The UON conducts both face to face (FF) and online (OL) classes that are intended to be identical. Given below are the distributions of the two groups in terms of marks scored in a statistics examination. The modal mark is known for each group and given as 68 for face to face and 64 for online students respectively.
|
Marks |
30- 40 |
40- 50 |
50- 60 |
60- 70 |
70- 80 |
80 – 90 |
90-100 |
Total |
|
F.F Students |
6 |
18 |
12 |
f1 |
18 |
f2 |
12 |
100 |
|
O.N Students |
5 |
15 |
f1 |
22 |
19 |
11 |
f2 |
100 |
a. Find the missing frequencies f1 and f2 for each.
b. Based on the mean mark justify who should be rewarded for good performance.
c. Based on Pearson’s second coefficient of skewness, compare and comment on skewness of the two groups, explaining what this implies with reference to the performance of each group
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