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Connecting the Dots... - Visualising Data

Grade 7CBSE

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

🔑Concepts

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Data collection is the process of gathering information in the form of numerical figures to provide specific insights.

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The Arithmetic Mean (or Average) is a representative value of a group of data, calculated by dividing the sum of observations by the total number of observations.

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The Range is the spread of the data, calculated as the difference between the highest and lowest values in a data set.

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The Mode is the value that appears most frequently in a given set of data. A data set can have more than one mode if multiple values have the same maximum frequency.

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The Median is the middle-most value when the data is arranged in ascending or descending order. If the number of observations nn is odd, the median is the (n+12)th\left(\frac{n+1}{2}\right)^{th} observation.

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Bar Graphs are visual representations where the length of bars of uniform width represents the frequency of variables. They are useful for comparison.

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Double Bar Graphs are used to compare two sets of data simultaneously, such as the marks of students in two different terms.

📐Formulae

Arithmetic Mean=Sum of all observationsNumber of observations\text{Arithmetic Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}}

Range=Highest Value−Lowest Value\text{Range} = \text{Highest Value} - \text{Lowest Value}

Median (for odd n)=(n+12)th observation\text{Median (for odd } n \text{)} = \left( \frac{n + 1}{2} \right)^{th} \text{ observation}

💡Examples

Problem 1:

The ages in years of 1010 teachers in a school are: 32,41,28,54,35,26,23,33,38,4032, 41, 28, 54, 35, 26, 23, 33, 38, 40. Find the range of the ages.

Solution:

Identify the highest and lowest ages. Highest age = 5454, Lowest age = 2323. Range = 54−23=3154 - 23 = 31. Using vertical subtraction: 54−2331\begin{array}{r} 54 \\ - 23 \\ \hline 31 \end{array}

Explanation:

To find the range, we subtract the smallest value from the largest value in the data set.

Problem 2:

Find the Mean of the first five whole numbers.

Solution:

The first five whole numbers are 0,1,2,3,40, 1, 2, 3, 4. Sum = 0+1+2+3+4=100 + 1 + 2 + 3 + 4 = 10. Number of observations = 55. Mean=105=2\text{Mean} = \frac{10}{5} = 2

Explanation:

The mean is the average of the values. We sum the first five whole numbers (starting from 00) and divide by 55.

Problem 3:

Find the Median and Mode of the following data: 13,16,12,14,19,12,14,13,1413, 16, 12, 14, 19, 12, 14, 13, 14.

Solution:

  1. Arrange in ascending order: 12,12,13,13,14,14,14,16,1912, 12, 13, 13, 14, 14, 14, 16, 19. 2. Mode: The value 1414 occurs three times (highest frequency), so Mode=14\text{Mode} = 14. 3. Median: There are n=9n = 9 observations. Median=(9+12)th term=5th term\text{Median} = \left( \frac{9+1}{2} \right)^{th} \text{ term} = 5^{th} \text{ term}. The 5th5^{th} term is 1414. Therefore, Median=14\text{Median} = 14.

Explanation:

The mode is the most frequent number, and the median is the center value after sorting the data.