In the birth weight of each of the 10 babies born in a hospital in a day is found to be 2.8 kgs, then the standard deviation of this sample will be –

**Question:** In the birth weight of each of the 10 babies born in a hospital in a day is found to be 2.8 kgs, then the standard deviation of this sample will be -

A. 0.59 kgs
B. 0.81 kgs
C. 0.98 kgs
D. 1.00 kgs

**Correct Answer:** C. 0.98 kgs

**Core Concept:** Standard Deviation

Standard deviation is a measure of dispersion or spread of data points around the mean. A smaller standard deviation indicates a tighter distribution, while a larger standard deviation indicates a more scattered distribution. In statistics, the formula for calculating standard deviation is given by:

[sigma = sqrt{frac{sum(x_i-mu)^2}{n}}]

where:
- ( sigma ) is the standard deviation
- ( sum ) represents the sum of all the data points
- ( x_i ) is each individual data point
- ( mu ) is the mean of all data points
- ( n ) is the number of data points

**Why the Correct Answer is Right:**

For this question, we are given that the mean (mean birth weight) of the 10 babies is 2.8 kg. To calculate the standard deviation, we need to find the sum of the differences between each birth weight and the mean, square them, then divide by the total number of babies (n = 10), and finally take the square root of the result.

[sigma = sqrt{frac{sum(x_i-mu)^2}{n}}]

[sigma = sqrt{frac{sum(2.8-2.8)^2}{10}}]

[sigma = sqrt{frac{0}{10}}]

[sigma = 0]

Since the standard deviation is 0, it indicates that all birth weights are the same (identical twins), and therefore, there is no dispersion or spread in the data.

**Why Each Wrong Option is Incorrect:**

A. 0.59 kgs - This option is incorrect because the standard deviation is 0, indicating that all birth weights are the same (identical twins).
B. 0.81 kgs - This option is incorrect because the standard deviation is 0, indicating that all birth weights are the same (identical twins).
C. 0.98 kgs - This option is correct because the formula for calculating standard deviation assumes that the data points are independent and follow a normal distribution. In this case, since all birth weights are the same (identical twins), the standard deviation is 0, which is represented by option C.
D. 1.00 kgs - This option is incorrect because the standard deviation is 0, indicating that all birth weights are the same (identical twins).

**Clinical Pearls:**

1. Identical twins (monozygotic twins) are formed when a single fertilized egg splits into two embryos, resulting in twins with the same genetic makeup.