Median weight of 100 children was 12 kgs. The standard detion was 3. Calculate the percent coefficient of variance:
**Core Concept:**
The percent coefficient of variance (CV) is a measure of the dispersion of a set of values, defined as the coefficient of variance (CV) divided by the standard deviation (SD). It is used to compare the variability of different datasets.
**Why the Correct Answer is Right:**
To calculate the percent coefficient of variance, we follow these steps:
1. Calculate the coefficient of variance (CV): (SD / Mean) x 100
2. Calculate the standard deviation (SD): sqrt(Σ((Xi - Mean)^2 / n)
3. Divide the coefficient of variance by the standard deviation and multiply by 100 to get the percent coefficient of variance.
In this question, we are given the median weight of 100 children as 12 kg and the standard deviation (SD):
Σ((Xi - Mean)^2 / n) = (12 - 12)^2 / 100 = 0 / 100 = 0
SD = sqrt(0) = 0
Now, calculate the coefficient of variance (CV):
CV = (0 / 12) x 100 = 0%
Finally, divide the coefficient of variance by the standard deviation and multiply by 100:
Percent coefficient of variance = (0 / 0) x 100 = 0%
**Why Each Wrong Answer is Incorrect:**
A. The calculation for this option is incorrect, as it includes the mean (12 kg), which is not needed to find the CV and SD.
B. The calculation for this option is also incorrect, as it includes the mean (12 kg) and does not take the square root of the sum of the squared deviations from the mean.
C. The calculation for this option is incorrect, as it includes the mean (12 kg).
D. The calculation for this option is incorrect, as it includes the mean (12 kg) and does not take the square root of the sum of the squared deviations from the mean.
**Why the Correct Answer (0%) is Right:**
The correct calculation for the percent coefficient of variance is:
Percent coefficient of variance = (CV / SD) x 100
Since we found that the SD is 0, the percent coefficient of variance is also 0%. This means that the mean weight (12 kg) is also the median (since the SD is 0), which indicates that all weights are the same and thus there is no variation among the weights.
**Core Concept:** The percent coefficient of variance is used to compare the variability of different datasets. A lower percent coefficient of variance indicates less variability and vice versa. In this case, the zero percent coefficient of variance indicates that all weights are the same, meaning there is no variation among the weights.
**Why the Correct Answer (0%) is Right:**
The correct calculation for the percent coefficient of variance is:
Percent coefficient of variance = (CV / SD) x 100
Since the SD is 0, the percent coefficient of variance is also 0%. This means that the mean (12 kg)