Week 2 Graded Assignment

Week 2 Graded Assignment


Statistics Graded Assignment


1. Which of the following statements is/are incorrect?

Options: (a) To represent the share of a particular category, bar chart is the most appropriate graphical representation. (b) The multiplication of the total number of observations and relative frequency of a particular observation should be equal to the frequency of that observation. (c) Mean can be defined for a categorical variable. (d) Mode of a categorical variable is the widest slice in a pie chart.

Answer: a, c Solution: To show the share of a particular category, a pie chart is the most appropriate graphical representation. Thus, option (a) is incorrect. Relative frequency for the ith observation is Rfi=fi/N Rf_i = f_i / N , so fi=Rfi×N f_i = Rf_i \times N . Thus, option (b) is correct. Mean cannot be defined for categorical data as meaningful mathematical operations are not possible. Thus, option (c) is incorrect. In a pie chart, the widest slice corresponds to the mode (highest frequency). Thus, option (d) is correct. Therefore, options (a) and (c) are correct (as the question asks for incorrect statements).


2. If the exam is for a total of 500 marks, then what is the aggregate distribution of marks in Physics, Maths and Biology?

(Refer to Figure 2.1.G, which shows: Physics 35%, Maths 18%, Biology 10%)

Answer: 315 Solution: Physics: 500×0.35=175 500 \times 0.35 = 175 Maths: 500×0.18=90 500 \times 0.18 = 90 Biology: 500×0.10=50 500 \times 0.10 = 50 Aggregate: 175+90+50=315 175 + 90 + 50 = 315


3. Choose the correct statement(s):

Options: (a) The pie chart is misleading because it does not obey the area principle. (b) The pie chart has round off errors. (c) The pie chart is not a misleading graph. (d) The slices of pie chart adds up to 100%.

Answer: c, d Solution: The pie chart obeys the area principle and the slices add up to 100%. Thus, options (c) and (d) are correct.


4. What is the combined relative frequency of the academy A, B and D?

(Refer to Table 2.1.G: Academy C has 50 players, E has 75 players; total 200 players.)

Answer: 0.375 (Range: 0.370, 0.380) Solution: Relative frequency for C: 50/200=0.25 50/200 = 0.25 Relative frequency for E: 75/200=0.375 75/200 = 0.375 Combined relative frequency for A, B, D: 1(0.25+0.375)=0.375 1 - (0.25 + 0.375) = 0.375


5. Median of the given data is:

Options: (a) Academy C (b) Academy E (c) Academy D (d) Median is not defined for the given data (e) Insufficient data

Answer: d Solution: The data is nominal and cannot be ordered, so median is not defined.


6. Mode of the given data is:

Options: (a) Academy C (b) Academy E (c) Academy D (d) Mode is not defined for the given data (e) Insufficient data

Answer: b Solution: Academy E has the highest frequency (75), so it is the mode.


7. Which of the following graphical representations is appropriate for the number of players in each academy for the given data in Table 2.1.G?

Options: (a) Bar chart (b) Pie chart (c) Pareto chart (d) Both bar chart and pareto chart

Answer: d Solution: Bar chart and Pareto chart are both appropriate for showing counts. Pie chart is for proportions.


8. The data of number of students sharing the same rank is collected. Which of the following is/are suitable to represent the collected data?

Options: (a) (plot with missing baseline) (b) (plot with correct baseline and order) (c) (plot with incorrect order of categories)

Answer: b Solution: Option (b) correctly preserves the order and is not misleading.


9. Choose the correct statement about categorical data:

Options: (a) Categorical data have measurement units. (b) Categorical data can take numerical values, but no meaningful mathematical operations can be performed on it. (c) Categorical data is quantitative in nature. (d) All of the above

Answer: b Solution: Categorical data can be coded numerically, but no meaningful mathematical operations can be performed.


10. How many students have secured B grade?

(Refer to Figure 2.2.G: B grade 32.5% of 80 students.)

Answer: 26 Solution: 80×0.325=26 80 \times 0.325 = 26


11. What is the ratio of the students secured C grade to the students secured A grade?

(Figure 2.2.G: C grade 22.5%, A grade 25% of 80 students.)

Answer: 0.9 Solution: C grade: 80×0.225=18 80 \times 0.225 = 18 A grade: 80×0.25=20 80 \times 0.25 = 20 Ratio: 18/20=0.9 18/20 = 0.9


This is the complete set of questions and solutions from the PDF1.


  1. Week_2_Graded_Solution.pdf ↩︎