Measures of central tendency: Mean, Median, Mode, Standard Deviation (केंद्रीय प्रवृत्ति: माध्य, माध्यिका, बहुलक और मानक विचलन) In Hindi
माध्य: माध्य, जिसे अंग्रेजी में “mean” कहा जाता है, एक संख्यात्मक डेटा सेट में सभी संख्याओं का औसत होता है। यह डेटा सेट के “केंद्र बिंदु” का अनुमान लगाने में मदद करता है।- माध्य = Σx / n
Measures of central tendency: Mean, Median, Mode, Standard Deviation In English
Mean (x̅ or μ): The mean is the average of all the numbers in a data set. It is calculated by adding all the values and dividing by the number of values.- Mean = \( \frac{sum of the values}{the number of values} \)
Direct Method | Assumed Mean Method | Step Deviation Method |
---|---|---|
x̅ = ∑ fixi / ∑ fiwhere, ∑fi is the sum of all frequencies | x̅ = a + ∑ fixi / ∑ fiwhere, a is Assumed mean di is equal to xi – a ∑fi the sum of all frequencies | x̅ = a + h∑ fixi / ∑ fiwhere, a is Assumed mean ui = (xi – a)/h h is Class size ∑fi the sum of all frequencies |
Types | Description |
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Median for Odd Number of Observations | If the number of observations (n) is odd, the median is the value at the (n + 1) / 2 position when the data is sorted in ascending order. |
Median for Even Number of Observations | If the number of observations (n) is even, the median is the average of the values at the n / 2th and (n / 2)th + 1 positions when the data is sorted in ascending order. |
- Median = [(n + 1)/2]th term
- Median = [(n/2)th term + {(n/2) + 1}th term] / 2
- Mode = Highest Frequency Term
- Mode = l + [(f1 + f0) / (2f1 – f0 – f2)] × h
- Mode = 3 Median – 2 Mean
- Range = Highest value – Lowest Value
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