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Tales by Dots and Lines - Visualising and Interpreting Data

Grade 8CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Data can be organized and visualized using different types of graphs. A Line Graph is particularly useful for showing how data changes continuously over a period of time, such as temperature variations or distance covered by a vehicle.

A line graph showing the relationship between time and distance with points connected by line segments.
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A Histogram is used for representing grouped frequency distributions where the data is continuous. There are no gaps between the bars, and the area of each bar represents the frequency of the corresponding class interval.

A histogram showing rectangular bars representing frequency without gaps between them.
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A Pie Chart or a Circle Graph shows the relationship between a whole and its parts. The size of each sector is proportional to the information it represents, calculated using the central angle formula.

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Double Bar Graphs are used to compare two sets of data simultaneously. For example, comparing the marks of a student in two different terms across various subjects.

📐Formulae

Class Size=Upper Limit−Lower Limit\text{Class Size} = \text{Upper Limit} - \text{Lower Limit}

Class Mark=Upper Limit+Lower Limit2\text{Class Mark} = \frac{\text{Upper Limit} + \text{Lower Limit}}{2}

Central Angle of a Sector=(Value of the ComponentTotal Value×360∘)\text{Central Angle of a Sector} = \left( \frac{\text{Value of the Component}}{\text{Total Value}} \times 360^\circ \right)

Probability of an Event P(E)=Number of outcomes that make an eventTotal number of outcomes of the experiment\text{Probability of an Event } P(E) = \frac{\text{Number of outcomes that make an event}}{\text{Total number of outcomes of the experiment}}

💡Examples

Problem 1:

In a class of 3030 students, 1212 like Mathematics, 99 like Science, and 99 like English. Calculate the central angle for Mathematics to represent this data on a Pie Chart.

Solution:

Total number of students = 3030. Number of students who like Mathematics = 1212. Central Angle=(1230×360∘)\text{Central Angle} = \left( \frac{12}{30} \times 360^\circ \right) Central Angle=(25×360∘)\text{Central Angle} = \left( \frac{2}{5} \times 360^\circ \right) Central Angle=2×72∘=144∘\text{Central Angle} = 2 \times 72^\circ = 144^\circ

Explanation:

To find the central angle, we divide the frequency of the specific component by the total frequency and multiply by the total degrees in a circle (360∘360^\circ).

Problem 2:

A die is thrown once. What is the probability of getting a prime number?

Solution:

Total outcomes when a die is thrown: S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\}. So, total outcomes = 66. Prime numbers on a die: E={2,3,5}E = \{2, 3, 5\}. So, number of favorable outcomes = 33. P(Prime Number)=36=12P(\text{Prime Number}) = \frac{3}{6} = \frac{1}{2}

Explanation:

The probability is calculated by identifying the subset of prime numbers within the sample space of a six-sided die.

Problem 3:

Find the class mark and class size for the class interval 150−200150 - 200.

Solution:

Lower Limit = 150150, Upper Limit = 200200. Class Size=200−150=50\text{Class Size} = 200 - 150 = 50 Class Mark=200+1502=3502=175\text{Class Mark} = \frac{200 + 150}{2} = \frac{350}{2} = 175

Explanation:

Class size is the difference between the limits, while the class mark is the midpoint (average) of the limits.

Problem 4:

The following line graph shows the temperature of a patient in a hospital recorded every hour. At what time was the patient's temperature 38.5∘C38.5^\circ C?

Line graph of patient temperature over time from 12 PM to 3 PM.

Solution:

38.5∘C occurs at 1:30 PM38.5^\circ C \text{ occurs at 1:30 PM}

Explanation:

Look at the y-axis (Temperature) and find the point between 3838 and 3939. Move horizontally to the right to find the corresponding point on the line. Then, move vertically down to the x-axis to find the time. The point lies exactly midway between 11 PM and 22 PM.

Problem 5:

A survey of 360360 people was made to find the type of music they like. If 10%10\% of the people like Semi-classical music, how many people were surveyed who liked this type?

Pie chart with a 10 percent sector highlighted for Semi-classical music.

Solution:

Number of people=10% of 360\text{Number of people} = 10\% \text{ of } 360 Number of people=10100×360=36\text{Number of people} = \frac{10}{100} \times 360 = 36

Explanation:

The percentage represents a part of the whole (360360 people). By multiplying the decimal or fractional form of the percentage by the total population, we find the specific count for that category.