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If the mean of a frequency distribution is 100 and the coefficient of variation is 45%, then what is the value of the variance?
  • a)
    2025
  • b)
    450
  • c)
    45
  • d)
    4.5
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the mean of a frequency distribution is 100 and the coefficient of ...
Concept:
Coefficient of variation = Standard Deviation/Mean
Variance = (Standard Deviation)2
Calculation:
Given coefficient of variation = 45% = 0.45
And mean = 100
As Coefficient of variation = Standard Deviation/Mean
0.45 = Standard Deviation/100
Standard Deviation = 100 × 0.45
SD = 45
∴ Variance = 452 = 2025
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Most Upvoted Answer
If the mean of a frequency distribution is 100 and the coefficient of ...
To find the value of the variance, we need to first understand what the coefficient of variation represents. The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean and multiplying by 100. It is often expressed as a percentage.

Given that the mean of the frequency distribution is 100 and the coefficient of variation is 45%, we can use this information to find the standard deviation.

Let's assume the standard deviation is represented by 's'.

The coefficient of variation (CV) can be calculated using the formula:

CV = (s / mean) * 100

Substituting the given values:

45% = (s / 100) * 100

Simplifying the equation:

0.45 = s / 100

Cross-multiplying:

s = 0.45 * 100

s = 45

Now that we have the value of the standard deviation, we can find the variance using the formula:

Variance = (standard deviation)^2

Substituting the value of the standard deviation:

Variance = 45^2

Variance = 2025

Therefore, the value of the variance is 2025.
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Community Answer
If the mean of a frequency distribution is 100 and the coefficient of ...
Concept:
Coefficient of variation = Standard Deviation/Mean
Variance = (Standard Deviation)2
Calculation:
Given coefficient of variation = 45% = 0.45
And mean = 100
As Coefficient of variation = Standard Deviation/Mean
0.45 = Standard Deviation/100
Standard Deviation = 100 × 0.45
SD = 45
∴ Variance = 452 = 2025
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Directions: Read the passages and choose the best answer to each question.PassageThe photoelectric effect is the emission of electrons from matter upon the absorption of electromagnetic radiation, such as ultraviolet radiation or X-rays. Electromagnetic radiation is made up of photons, which can be considered finite packets of energy at various levels. Photons have properties attributed to both particles and waves. This phenomenon is known as the wave-particle duality.The photoelectric effect is especially noticeable when dealing with metals. When a metallic surface is exposed to electromagnetic radiation that is above the minimum energy threshold (which is specific to the type of surface and material), photons are absorbed and electrons are emitted. No electrons are emitted for radiation with energy frequencies below that of the threshold, as the electrons are unable to gain sufficient energy to overcome the attractive forces within the metal. A scientist wishing to measure the photoelectric effect so as to further understand the nature of photons conducted the following experiments.Experiment 1Wishing to measure the energy required to produce the photoelectric effect on a surface of a sheet of copper, the scientist directed a beam of radiation at different frequencies (energies)—measured in Hertz (Hz)—onto the surface.After 5 minutes, the charge—measured in volts (V)—of the sheet of metal was recorded. This was done because if electrons were emitted from the surface, the metal would take on a positive charge. The results were recorded in Table 1.Experiment 2Solar cells used to generate electricity are based on the concept of the photoelectric effect; however, the goal of the cell is to capture the emitted electron and create an electric current. The scientist measured the effects of different frequencies (in Hz) of radiation on the current (in V) generated by a certain solar cell. The results were recorded in Table 2.Q.Which of the following procedures would result in the most accurate values for the effect of frequency of radiation on the photoelectric effect (Experiment 1)?

Directions: Read the passages and choose the best answer to each question.PassageThe photoelectric effect is the emission of electrons from matter upon the absorption of electromagnetic radiation, such as ultraviolet radiation or X-rays. Electromagnetic radiation is made up of photons, which can be considered finite packets of energy at various levels. Photons have properties attributed to both particles and waves. This phenomenon is known as the wave-particle duality.The photoelectric effect is especially noticeable when dealing with metals. When a metallic surface is exposed to electromagnetic radiation that is above the minimum energy threshold (which is specific to the type of surface and material), photons are absorbed and electrons are emitted. No electrons are emitted for radiation with energy frequencies below that of the threshold, as the electrons are unable to gain sufficient energy to overcome the attractive forces within the metal. A scientist wishing to measure the photoelectric effect so as to further understand the nature of photons conducted the following experiments.Experiment 1Wishing to measure the energy required to produce the photoelectric effect on a surface of a sheet of copper, the scientist directed a beam of radiation at different frequencies (energies)—measured in Hertz (Hz)—onto the surface.After 5 minutes, the charge—measured in volts (V)—of the sheet of metal was recorded. This was done because if electrons were emitted from the surface, the metal would take on a positive charge. The results were recorded in Table 1.Experiment 2Solar cells used to generate electricity are based on the concept of the photoelectric effect; however, the goal of the cell is to capture the emitted electron and create an electric current. The scientist measured the effects of different frequencies (in Hz) of radiation on the current (in V) generated by a certain solar cell. The results were recorded in Table 2.Q.Which of the following assumptions did the scientist probably make in choosing these experiments to test the nature of photons?

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If the mean of a frequency distribution is 100 and the coefficient of variation is 45%, then what is the value of the variance?a)2025b)450c)45d)4.5Correct answer is option 'A'. Can you explain this answer?
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