Basic Statistics · Unit 3
Data Presentation and Visualization
Exam-focused notes for Data Presentation and Visualization (Basic Statistics, STA154): what the TU syllabus asks and how it has actually been tested, with 11 solved past questions from this unit.
What this unit covers
- Frequency distributions and tables
- Histogram construction
- Frequency polygon and frequency curve
- Bar diagrams and Pareto diagrams
- Pie charts
- Box and whisker plots
- Five number summary
Bar diagrams and Pareto diagrams
Differentiate Pareto chart and a bar diagram. [5]
Bar Diagram: - A basic statistical graph that displays data using rectangular bars of equal width - Bars are arranged side-by-side or in groups - Used to compare quantities across different categories - Primarily for simple data comparison and visualization...
Full solved answer →The following table shows the mode of transport used by 400 students of a school. Represent the following information on the bar diagram and Pareto diagram.
| Mode of transport | Bus | Bicycle | On foot | By car |
|---|---|---|---|---|
| No. of students | 200 | 100 | 80 | 20 |
[5]
Mode of transport Bus Bicycle On foot By car --------------- No. of students 200 100 80 20 Total students $= 200 + 100 + 80 + 20 = 400$ --- A bar diagram represents each category by a rectangular bar whose height is proportional to its frequency. Bars are o...
Full solved answer →Construct bar diagram and Pareto diagram of the following information.
| Brand | Dell | Acer | Lenovo | HP | Total |
|---|---|---|---|---|---|
| No. of Sales | 50 | 100 | 40 | 60 | 250 |
[5]
Brand Dell Acer Lenovo HP Total -------------------------------------- No. of Sales 50 100 40 60 250 --- In a bar diagram, each brand is shown as a separate rectangular bar whose height equals its number of sales. Bars are of equal width with equal gaps. - ...
Full solved answer →Pie charts
In a survey of 50 IT students, the following programming languages were preferred: Python (20), Java (15), C++ (10), and JavaScript (5). Create a pie chart representing the preferences. [5]
Total students surveyed = 50 Language Count ----------------- Python 20 Java 15 C++ 10 JavaScript 5 Check: $20 + 15 + 10 + 5 = 50$ ✓ The angle for each sector is computed as: $$\text{Angle} = \frac{\text{Count}}{\text{Total}} \times 360°$$ Python: $$\frac{2...
Full solved answer →The following table shows the numbers of hours spent by a child on different events on a working day. Represent the adjoining information on a pie chart.
| Activity | No. of hours |
|---|---|
| School | 6 |
| Sleep | 8 |
| Playing | 2 |
| Study | 4 |
| T.V. | 1 |
| Others | 3 |
[5]
Activity No. of hours ------------------------ School 6 Sleep 8 Playing 2 Study 4 T.V. 1 Others 3 $$\text{Total} = 6 + 8 + 2 + 4 + 1 + 3 = 24 \text{ hours}$$ Formula: $$\text{Central Angle} = \frac{\text{Hours for activity}}{\text{Total hours}} \times 360°$...
Full solved answer →Five number summary
The time taken (in seconds) to complete a file transfer operation is recorded for 11 sessions. Calculate the five-number summary and construct a box plot. 100, 120, 110, 115, 130, 105, 125, 122, 112, 108, 135 [5]
Transfer times (seconds), $n = 11$: $$100, 120, 110, 115, 130, 105, 125, 122, 112, 108, 135$$ $$100,\ 105,\ 108,\ 110,\ 112,\ 115,\ 120,\ 122,\ 125,\ 130,\ 135$$ - Min = $100$ - Max = $135$ With $n = 11$, position $= \frac{n+1}{2} = 6$th value. $$\text{Medi...
Full solved answer →Drive D of a computer having 25 folders contain the following number of files. (a) List the five number summaries (b) Construct a box-plot for the data (c) Are the data skewed? 4, 0, 5, 2, 3, 1, 4, 3, 2, 3, 4, 3, 1, 6, 3, 2, 3, 4, 2, 1, 0, 3, 2, 5, 4 [5]
Number of files in 25 folders: $$4, 0, 5, 2, 3, 1, 4, 3, 2, 3, 4, 3, 1, 6, 3, 2, 3, 4, 2, 1, 0, 3, 2, 5, 4$$ $n = 25$ Step 1: Sort the data $$0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 6$$ Let me verify the counts: - 0 appears 2...
Full solved answer →Box and whisker plots
Write short note on the following: a) Use of Box and whisker plot. b) Parameter and Statistic. [5]
A box and whisker plot (or boxplot) is a graphical method used to display the distribution and spread of numerical data. Its main uses include: - Visual Summary of Data: Displays five-number summary - minimum, Q1 (first quartile), median (Q2), Q3 (third qua...
Full solved answer →Write short notes on : a.) Box and whisker plot. Write short notes on : b.) Census survey and sample survey [2.5+2.5]
A box and whisker plot (or boxplot) is a graphical method for displaying the distribution and spread of numerical data based on five-number summary statistics. Components: - Minimum value: The smallest data point (or lower whisker endpoint) - First Quartile...
Full solved answer →Write short notes on the following: a.)Box and whisker plot b.) Choice of appropriate measure of central tendency [5]
A box and whisker plot (or boxplot) is a graphical method for displaying the distribution and spread of numerical data using five-number summary statistics. Components: - Minimum value: The smallest observation in the dataset - First Quartile (Q1): The 25th...
Full solved answer →Histogram construction
Construct histogram, frequency polygon and frequency curve of the following frequency distribution.
| Circumference (cm) | 50 | 55 | 54 | 52 | 37 | 52 | 53 | 47 |
|---|---|---|---|---|---|---|---|---|
| Weight (gram) '00' | 12 | 20 | 15 | 17 | 50 | 10 | 15 | 14 |
[5]
The data is presented as paired values of Circumference (cm) and Weight (gram, in hundreds i.e. '00'): Circumference (cm) 50 55 54 52 37 52 53 47 --------------------------- Weight (gram '00') 12 20 15 17 50 10 15 14 Important interpretation note: This is N...
Full solved answer →Make Unit 3 stick
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