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Connecting the Dots... - Representative Values

Grade 7CBSE

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

🔑Concepts

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Representative values, also known as measures of central tendency, help us summarize a large set of data with a single value.

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The Arithmetic Mean (or simply mean) is the average of a set of numbers, calculated by dividing the sum of the observations by the total number of observations.

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The Range is the difference between the highest and the lowest observation in a data set, representing the spread of the data.

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The Mode is the value that appears most frequently in a given data set. A data set can have more than one mode (multimodal) or no mode at all.

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The Median is the middle value of a data set when the observations are arranged in ascending or descending order. It divides the data into two equal halves.

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For a data set with nn observations (where nn is odd), the median is the (n+12)th\left(\frac{n+1}{2}\right)^{\text{th}} observation.

📐Formulae

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

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

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

💡Examples

Problem 1:

Find the Mean and Range of the following marks obtained by 5 students in a test: 23,35,48,30,2523, 35, 48, 30, 25.

Solution:

Sum of marks = 23+35+48+30+25=16123 + 35 + 48 + 30 + 25 = 161 Number of students = 55 Mean=1615=32.2\text{Mean} = \frac{161}{5} = 32.2

To find the Range: Highest mark=48\text{Highest mark} = 48 Lowest mark=23\text{Lowest mark} = 23 Range=48−23=25\text{Range} = 48 - 23 = 25

Explanation:

The mean is calculated by finding the total sum of marks and dividing by the count of students. The range is the gap between the maximum and minimum values.

Problem 2:

Find the mode of the following set of numbers: 1,1,2,4,3,2,1,2,2,41, 1, 2, 4, 3, 2, 1, 2, 2, 4.

Solution:

Let's count the frequency of each number:

  • 11 occurs 33 times
  • 22 occurs 44 times
  • 33 occurs 11 time
  • 44 occurs 22 times

Since 22 occurs the most frequently (44 times), the Mode is 22.

Explanation:

The mode is the observation with the highest frequency in the data set.

Problem 3:

Find the median of the data: 24,36,46,17,18,25,3524, 36, 46, 17, 18, 25, 35.

Solution:

First, arrange the data in ascending order: 17,18,24,25,35,36,4617, 18, 24, 25, 35, 36, 46

Here, the number of observations n=7n = 7 (which is odd). Median=(7+12)th observation\text{Median} = \left(\frac{7+1}{2}\right)^{\text{th}} \text{ observation} Median=4th observation\text{Median} = 4^{\text{th}} \text{ observation}

The 4th4^{\text{th}} observation in the sorted list is 2525. Therefore, Median=25\text{Median} = 25.

Explanation:

The median is the central value of the ordered data set. Since there are 7 terms, the 4th term is exactly in the middle.