Introduction To Statistics Assignment, SMU, Singapore: Using the frequency distribution method, provide an arrangement or use a table that groups raw data into intervals

Question 1. Frequency distribution

Using the frequency distribution method, provide an arrangement or use a table that groups raw data into intervals or classes and records the number of observations (frequency) in each class. The information given would be as follows: A class Science test was recently conducted. We have obtained the raw marks.
The class test result is now recorded and the marks are given below:
94 42 313 49 194 212 19 140 16 120
105 116 29 58 167 163 29 88 302 101
187 155 106153 69 105 20 88 97 64
49 202170 217 19 313 307219 113 74
45 141 44 293 104 82 25 84 43 86
100 29 212 28 10 15 25 157 209 28
a). Provide the answer with your solution given.
b) Using the Frequency Distribution method, calculate and present your answer to demonstrate how marks are obtained.

Question 2. The measure of Central Tendency
Part |:
An Individual Observation of a problem is given below. Student is required to find the mean and it’s n number (where n = no of numbers). Using a relevant formula, find the mean of the set of numbers: 33, 41, 25, 30, 35.
a) Provide a solution with your answer by calculating the quantitative value of
sigma;
b) Provide your answer using the discrete series method and using the mean with a relevant formula.

Part Il:

The table below shows the scores in a class test. The marks had been corrected to the nearest mark.

Marks: 10-19  20-29  30-39  40-49  50 – 59
Freq :       2            8          12          14            5

a) Calculate the median by using a relevant formula.

c) Find the Median by using the graphical method. You are advised to draw the Cumulative Frequency Curve and Plot the cumulative frequency (cf) against it upper boundaries

Question 3. Measure of Dispersion

By referring to the table below, calculate by using the appropriate formula and finding the mean and the standard deviation below:

Mass (kg)    10-20  20-30  30-40
Frequency    2          5              3

Question 4. Sampling Distributions

a) Discuss what is Sampling Errors.
b} Discuss the nature or the types of data collection by using Primary data and
secondary data collection. You are to provide at least two examples each.
c) Provide what are the advantages and disadvantages of face-to-face interviews? You are to provide two examples each.
d) Discuss what is cluster sampling?