measures of central tendency (mean median and mode)

measures of central tendency (mean median and mode)

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  Measures of CentralTendency UNDERSTANDING MEAN, MEDIAN, MODE by- ansari shagufta
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  Introduction • Measures ofCentral Tendency are statistical tools used to determine a single value that represents the center or typical value of a dataset. • Helps in summarizing large amounts of data by identifying a central point. • There are 3 main types: • Mean • Median • Mode
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  Mean • Definition: • TheMean, also known as the Arithmetic average, is a measure of central tendency that represents the sum of all values in a dataset divided by the total number of values. • Formula: • where, x is the value of each data • n is the total number of values • Example: • Consider a dataset: 5, 10, 15, 20, 25 • Step 1: Sum of values: 5+10+15+20+25=75 • Step 2: Total number of values = 5 • Step 3: By applying formula: 75/5 = 15 • Mean = 15
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  Characteristics • Based onall data points. • Affected by extreme values (outliers). • Suitable for continuous data, not suitable for nominal data. • Can be used for both sample and population data.
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  Uses In Education: Average marksof students Schools and universities use mean to compare students’ performance, assess overall class progress, and set academic standards. In Economics: Per Capita Income Economists use mean to calculate the average income of a population, known as per capita income. In Business: Average Sales and Revenues Businesses calculate the mean sales or revenue over a period to understand trends.
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  Median • Definition: • TheMedian is the middle value of an ordered dataset. • Steps to calculate median: • 1. Arrange the data in ascending order. • 2. Determine the middle value • 3. If the number of observations (N) is odd, the median is the middle value. • 3.1. If N is even, the median is the average of the two middle values. • Example: • Case 1: When N is Odd • Consider the dataset: 5, 8, 12, 15, 18 Median = 12 • Case 2: When N is Even • Consider the dataset: 3, 7, 10, 14, 20, 25 • Middle two values = 10 and 14 Median = (10 + 14) / 2 = 12
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  Characteristics • Not affectedby extreme values (outliers). • Represents the central location of data. • Works well for continuous data • Works for both small and large data sets.
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  Uses In Income Distribution: MedianSalary The median salary reflects what a “typical” person earns. Salaries are often uneven due to different incomes. In Housing : Median House Prices Property prices in a city can be highly uneven due to differences in luxury properties and upper class. In Education: Median Test Scores The median provides a fairer representation of the students’ typical performance.
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  Mode Definition: • The modeis the value that appears most frequently in a dataset. Example: • Consider the dataset: 7, 8, 9, 9, 10, 10, 10, 11, 12 Mode = 10 Types of Modes: Unimodal – A dataset with one mode. Bimodal - A dataset with two mode. Multi modal - A dataset with more than two mode.
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  Characteristics • Represents themost frequent value. • Can be used for both numerical and categorical data. • Can have one or multiple values. • Works well for large datasets such as customer preferences, election results, or market trends. • Not affected by extreme values.
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  Uses In Business &Marketing: identifying popular products Helps in finding out which product, service, or brand is most preferred by customers. In Education: most common grades or test scores It helps to determine most common grade in exams. In Healthcare: Most Common Medical Conditions & Blood Types Track the most common illnesses, symptoms or treatments.
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  Conclusion • Choosing theRight Measure: • Use Mean → When data is evenly distributed and continuous (e.g., average test scores, income). • Use Median → When data has outliers or is uneven (e.g., house prices, salaries). • Use Mode → When analysing categorical data or identifying trends (e.g., favourite product, common defect). • Understanding these three measures helps in making informed decisions in various fields like education, business, healthcare, and social sciences.
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