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Statistics harmonic mean marks 30-40 ,40-50,50-60,60-70,70-80,80-90,90-100 Frequency 15,13,8,6,15,7,6?
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Statistics harmonic mean marks 30-40 ,40-50,50-60,60-70,70-80,80-90,90...
Statistics: Harmonic Mean



  1. Introduction

    2. The harmonic mean is a measure of central tendency that is used to find the average of a set of numbers. Unlike the arithmetic mean, which is the sum of all the numbers divided by the count, the harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of the numbers. It is often used in situations where the rates or ratios are involved, such as speed, time, or efficiency.

  2. Given Data

    3. The given data represents the frequency distribution of marks in different ranges: 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, and 90-100. The corresponding frequencies for each range are 15, 13, 8, 6, 15, 7, and 6, respectively.

  3. Calculating Harmonic Mean

    4. To calculate the harmonic mean for this data, we need to follow these steps:

    1. Find the reciprocal of each value in the data set. For example, for the range 30-40, the reciprocal is 1/35.

    2. Calculate the arithmetic mean of these reciprocals by summing them up and dividing by the count. For example:
    (1/35 + 1/45 + 1/55 + 1/65 + 1/75 + 1/85 + 1/95) / 7

    3. Take the reciprocal of the result obtained in step 2 to find the harmonic mean.

  4. Calculating Harmonic Mean for the Given Data

    5. Let's calculate the harmonic mean for the given data using the steps mentioned above:

    1. Reciprocals of the ranges:
    1/35, 1/45, 1/55, 1/65, 1/75, 1/85, 1/95

    2. Arithmetic mean of reciprocals:
    (1/35 + 1/45 + 1/55 + 1/65 + 1/75 + 1/85 + 1/95) / 7 = 0.0363

    3. Harmonic mean:
    1 / 0.0363 ≈ 27.5

    Therefore, the harmonic mean of the given data is approximately 27.5.

  5. Interpretation

    6. The harmonic mean of 27.5 suggests that the average mark in the given data set, considering the frequency distribution, is around 27.5. This measure takes into account the different ranges and their corresponding frequencies, providing a more accurate representation of the average mark. It is particularly useful when dealing with rates or ratios, as it gives more weight to the smaller values in the data set.



Conclusion

The harmonic mean is a statistical measure used to find the average of a set of numbers in situations where rates or ratios are involved. It is calculated by taking the reciprocal of each value in the data set, finding the arithmetic mean of these reciprocals, and then taking the reciprocal of the result. In the given data of marks in different ranges, the harmonic mean was calculated to be approximately
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Statistics harmonic mean marks 30-40 ,40-50,50-60,60-70,70-80,80-90,90-100 Frequency 15,13,8,6,15,7,6?
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Statistics harmonic mean marks 30-40 ,40-50,50-60,60-70,70-80,80-90,90-100 Frequency 15,13,8,6,15,7,6? for Commerce 2024 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about Statistics harmonic mean marks 30-40 ,40-50,50-60,60-70,70-80,80-90,90-100 Frequency 15,13,8,6,15,7,6? covers all topics & solutions for Commerce 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Statistics harmonic mean marks 30-40 ,40-50,50-60,60-70,70-80,80-90,90-100 Frequency 15,13,8,6,15,7,6?.
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