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Data Handling - Construction and Interpretation of Bar Graphs and Double Bar Graphs

Grade 7ICSE

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

🔑Concepts

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A Bar Graph is a visual representation of data using rectangular bars of uniform width, where the height or length of each bar is proportional to the value it represents. The bars are usually drawn with equal gaps between them.

A simple bar graph showing three categories A, B, and C with heights 60, 90, and 40 respectively.
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Double Bar Graphs are used to compare two different sets of data on the same categories simultaneously. For example, comparing the rainfall in two different years for the same months. A legend (key) is used to differentiate between the two data sets.

A double bar graph showing two sets of data for two items, side by side.
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The Scale of a graph is the ratio used to represent large numbers with smaller units on the axis. For example, if 1 unit length=10 students1 \text{ unit length} = 10 \text{ students}, then a bar of 5 units5 \text{ units} represents 5050 students.

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Interpretation involves reading the graph to find the minimum value, maximum value, and the difference between categories. It helps in making predictions and identifying trends in the data.

📐Formulae

Mean (Average)=Sum of all observationsTotal number of observations\text{Mean (Average)} = \frac{\text{Sum of all observations}}{\text{Total number of observations}}

Range=Maximum Value−Minimum Value\text{Range} = \text{Maximum Value} - \text{Minimum Value}

Height of a Bar (in units)=Value of DataValue of 1 Unit on Scale\text{Height of a Bar (in units)} = \frac{\text{Value of Data}}{\text{Value of 1 Unit on Scale}}

Scale=Maximum Data ValueNumber of units available on the axis\text{Scale} = \frac{\text{Maximum Data Value}}{\text{Number of units available on the axis}}

💡Examples

Problem 1:

The number of books sold by a library in four days is: Monday: 4545, Tuesday: 3030, Wednesday: 5555, and Thursday: 4040. If the graph is drawn with a scale of 1 unit=5 books1 \text{ unit} = 5 \text{ books}, calculate the height of the bar for Wednesday and find the range of books sold.

Solution:

  1. To find the height of the bar for Wednesday: Height=Value for WednesdayScale=555=11 units\text{Height} = \frac{\text{Value for Wednesday}}{\text{Scale}} = \frac{55}{5} = 11 \text{ units}
  2. To find the range: Range=Maximum Value−Minimum Value=55−30=25 books\text{Range} = \text{Maximum Value} - \text{Minimum Value} = 55 - 30 = 25 \text{ books}

Explanation:

The height of the bar is calculated by dividing the data value by the chosen scale. The range provides the difference between the highest and lowest values in the data set.

Problem 2:

In a double bar graph comparing the marks of Rahul in Term 1 and Term 2: Maths (Term 1: 8080, Term 2: 9090), Science (Term 1: 7575, Term 2: 8585), and English (Term 1: 7070, Term 2: 6565). Calculate the total marks for Term 2 and the improvement in Maths.

Solution:

  1. Total marks for Term 2: 90(Maths)+85(Science)+65(English)=24090 (\text{Maths}) + 85 (\text{Science}) + 65 (\text{English}) = 240
  2. Improvement in Maths: Term 2−Term 1=90−80=10 marks\text{Term 2} - \text{Term 1} = 90 - 80 = 10 \text{ marks}

Explanation:

For a double bar graph, we extract the values for one specific data series (Term 2) by identifying its corresponding bars using the legend, and then sum them. Improvement is the positive difference between the two terms.

Problem 3:

The following table shows the number of cycles sold by a shopkeeper over three months: January: 120120, February: 180180, and March: 150150. Draw a bar graph and determine which month had sales 1.51.5 times that of January.

Bar graph showing cycle sales for January (120), February (180), and March (150).

Solution:

  1. Let's choose a scale: 1 cm=30 cycles1 \text{ cm} = 30 \text{ cycles}.
  2. Height for January = 12030=4 units\frac{120}{30} = 4 \text{ units}.
  3. Height for February = 18030=6 units\frac{180}{30} = 6 \text{ units}.
  4. Height for March = 15030=5 units\frac{150}{30} = 5 \text{ units}.
  5. Sales for Jan = 120120. 1.5×120=1801.5 \times 120 = 180. February has 180180 sales.

Final Answer: February.

Explanation:

By comparing the height of the bars, we see February is 66 units high while January is 44 units. Since 6=1.5×46 = 1.5 \times 4, the visual confirms the calculation.

Problem 4:

A school sports day tracks the number of Gold medals won by two houses in three sports: Cricket (House A: 44, House B: 66), Football (House A: 88, House B: 55), and Basketball (House A: 55, House B: 55). Use a double bar graph to identify in which sport House B performed better than House A.

Double bar graph comparing medals won by House A and House B in three sports.

Solution:

  1. Comparing categories:
  • Cricket: House B (66) > House A (44).
  • Football: House A (88) > House B (55).
  • Basketball: House A (55) = House B (55).
  1. From the graph, the bar for House B is higher than House A only in Cricket.

Final Answer: Cricket.

Explanation:

In a double bar graph, we look for categories where the second bar (House B) is taller than the first bar (House A).