Chapter 4, Problem 4.4P

(a)

Interpretation Introduction

Interpretation:

The mean of the $16$ values present on the left and right side of the given table 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 $16$ values present on the left and right side of the given table

(b)

Interpretation Introduction

Interpretation:

The standard deviation of the $16$ values present on the left and right side of the given table 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 $16$ values present on the left and right side of the given table

(c)

Interpretation Introduction

Interpretation:

The standard deviation of the mean values for sets of $4$ candies to the sets of $16$ candies has to be calculated.

The predicted standard deviation has to be compared with the standard deviation in (b)

Concept Introduction:

Standard deviation of the mean:

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

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