91影视

Thedata on CeO2 particle sizes (nm) under certain experimental conditionsis provided as,

a.

The number of observations that are less than 5 is,

\(5 + 15 + 27 + 34 = 81\)

The total number of observations is 131.

The proportion of observations that are less than 5 is computed as,

\(\frac{{81}}{{131}} = 0.618\)

Thus, the proportion of observations that are less than 5 is approximately 0.618.

b.

The number of observations that are at least 6 is,

\(7 + 2 + 4 + 1 = 14\)

The total number of observations is 131.

The proportion of observations that are at least 6 is computed as,

\(\frac{{14}}{{131}} = 0.107\)

Thus, the proportion of observations that are at least 6 is approximately 0.107.

c.

The relative frequency is computed as,

\({\bf{relative frequency = }}\frac{{{\bf{frequency}}}}{{{\bf{Total}}\;{\bf{number}}\;{\bf{of}}\;{\bf{observations}}}}\)

The table representing the relative frequency is computed as,

Steps to construct a histogram are,

1) Determine the frequency or the relative frequency.

2) Mark the class boundaries on the horizontal axis.

3)Draw a rectangle on the horizontal axis corresponding to the frequency or relative frequency.

The histogram is represented as,

Observing the shape of the graph, it can be inferred that the graph is not exactly symmetric as it has an elongated tail in the right.

d.

The density value is computed as,

\({\bf{density = }}\frac{{{\bf{Relative}}\;{\bf{frequency}}}}{{{\bf{class}}\;{\bf{width}}}}\)

The table representing the densities is provided as,

Following the above steps, the histogram is represented as,

Comparing the above two histograms, there does not appear any change in both the diagrams.