Chapter 4, Problem 4.3P

(a)

Interpretation Introduction

Interpretation:

The mean of the ratio of number of atoms of the isotopes of $\text{G}\text{a}$ and $\text{G}\text{a}$ has to be calculated.

Concept Introduction:

Mean:

The Mean or the arithmetic mean ( $\overline{x}$) is given as the summation of measured values divided by the number of measurements (n). Mean is also called as average.

$\overline{x}=\frac{{\displaystyle \sum _i{x}_i}}{n}$

To Calculate: The mean of the ratio of number of atoms of the isotopes of $\text{G}\text{a}$ and $\text{G}\text{a}$

(b)

Interpretation Introduction

Interpretation:

The standard deviation of the ratio of number of atoms of the isotopes of $\text{G}\text{a}$ and $\text{G}\text{a}$ has to be calculated.

Concept Introduction:

Standard deviation:

Standard deviation measures how closely the data are clustered about the mean.

The standard deviation (s) is given by the formula:

$s=\sqrt{\frac{{\displaystyle \sum _i{(x_i-\overline{x})}^2}}{n-1}}$

To Calculate: The standard deviation of the ratio of number of atoms of the isotopes of $\text{G}\text{a}$ and $\text{G}\text{a}$

(c)

Interpretation Introduction

Interpretation:

The variance of the ratio of number of atoms of the isotopes of $\text{G}\text{a}$ and $\text{G}\text{a}$ has to be calculated.

Concept Introduction:

Variance:

The square of the standard deviation is called the variance.

To Calculate: The variance of the ratio of number of atoms of the isotopes of $\text{G}\text{a}$ and $\text{G}\text{a}$

(d)

Interpretation Introduction

Interpretation:

The standard deviation of the mean of the ratio of number of atoms of the isotopes of $\text{G}\text{a}$ and $\text{G}\text{a}$ has to be calculated.

Concept Introduction:

Standard deviation of the mean:

Standard deviation of the mean of sets of n values is:

${\sigma }_n=\frac{\sigma }{\sqrt{n}}$

To Calculate: The standard deviation of the mean of the ratio of number of atoms of the isotopes of $\text{G}\text{a}$ and $\text{G}\text{a}$

(e)

Interpretation Introduction

Interpretation:

The mean and standard deviation has to be written together with appropriate number of significant digits.

Concept Introduction:

Significant Figures:

While reporting a reading of a measurement, the digits that are considered to be significant irrespective of the place of location of decimal point are called significant figures.

All the digits in a measurement except zero are considered significant, whereas zero is considered as significant only when it lies in the middle of the digit or at the end of number on the right-hand side of a decimal point.

To Write: The mean and standard deviation together with appropriate number of significant digits.