Question

PURPOSE

The purpose of this assignment is to develop learners’ ability to analyse data and discuss the differences between the types of statistics.

REQUIREMENT

The following data represent the marks of the Statistic subject obtained by 25 students in mid semester examination. Use this data to answer the following questions:

1	2	4	4	5
6	7	9	9	12
5	12	15	17	20
21	23	23	25	26
27	27	28	29	29

Based on the information from the table above:

1. Discuss at least four (4) clear differences between quantitative and qualitative data. Provide sufficient and relevant examples.

2. Classify and analyse the data above using the methods correctly. Show clearly the raw result of the data analysis as follows:

1. Frequency distribution uses “0 but less than 5”
2. Class-boundary and Class Mid-point
3. Relative Frequency
4. Cumulative Frequency

(iii)      Based on the data, prepare the following:

• Arrange the results clearly in order
• Use tables to present the results
• Use suitable graphs to present the results.

4. Provide a clear and detailed write up to present the data from the analysis.  

[Total: 60 marks]

Answer 1

For the data set given, data is marks of 25 students in mid semester examination

i. Quantitative data are measures of values or counts and are expressed as numbers whereas qualitative data are measures of types and may be represented by name symbol or anumber code
hence four difference between quantitative and qualitative data re as under
a. qualitative data gives us information about quality of something, quantitative data gives us numerical quality
b. qualitative data can be numberical or text or both, quantitative data is always numericals, and may or may not havew accompanying units
c. Statistical ananlysis may be directly applied to quantitative data where as qualitative data needs preprocessing before it can be processed for statistical analysis
d. quantitative data follows laws of algebra where as qualitative data may or may not follow laws of algebra

ii. from the above definition and from the given numberical data, we can easily say that the given data is quantitative data as it give us quantity of marks of students
the statistical analysis of the problem is as under :
a. we will take class width of 4
b. class boundaries
0 - 5, mid point 2.5, frequency 4
5 - 10, mid point 7.5, frequency 6
10 - 15, mid point 12.5, frequency 2
15 - 20, mid point 17.5, frequency 2
20 - 25, mid point 22.5, frequency 4
25 - 30 , mid point 27.5, frequency 7
  
c. relative frequency is obtained by dividing frequcny with total number of events i.e. 25
0 - 5, mid point 2.5, relative frequency 4/25 = 0.16
5 - 10, mid point 7.5, frelative frequency 6/25 = 0.24
10 - 15, mid point 12.5, relative frequency 2/25 = 0.08
15 - 20, mid point 17.5, relative frequency 2/25 = 0.08
20 - 25, mid point 22.5, relative frequency 4/25 = 0.16
25 - 30 , mid point 27.5, relative frequency 7/25 = 0.28
  
d. cumulative frequency is obtained by adding all previous ones

0 - 5, mid point 2.5, cumulative frequency 4
5 - 10, mid point 7.5, cumulative frequency 10
10 - 15, mid point 12.5,cumulative frequency 12
15 - 20, mid point 17.5,cumulative frequency 14
20 - 25, mid point 22.5,cumulative frequency 18
25 - 30 , mid point 27.5,cumulative frequency 25
  
iii.
based on above analysis
a. in order results are
1, 2, 4, 4, 5, 5, 6, 7, 9, 9, 12, 12, 15, , 17, 20, 21, 23, 23, 25, , 26, 27, 27, 28, 29, 29
  
b. graphs are
frewucny distribution graph

as we can see we have made the frequency distribution histogram in excel where we had to make bins from 1 and above due to which the frequency distribution is changes as upper limits are now included and have hence increased by 1 from the theory we calculated