Question

the accompanying data represent the approximate population, in millions, of the 20 most populous cities in the world.

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$$\begin{array}{|c|c|c|c|c|} \\hline 13.7 & 11.7 & 10.1 & 8.8 & 7.9 \\\\ \\hline 13.1 & 11.4 & 9.6 & 8.5 & 7.7 \\\\ \\hline 12.5 & 11.3 & 9.1 & 8.1 & 7.2 \\\\ \\hline 12.2 & 10.6 & 9.1 & 8.1 & 7.2 \\\\ \\hline \\end{array}$$

use these data to construct a frequency distribution with a first class of 7.0 - 7.9. fill in the missing classes and the frequency for each class below.

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$$\begin{array}{c|c} \\text{population (millions of people)} & \\text{number of cities} \\\\ \\hline 7.0 - 7.9 & \\\\ \\hline \\square - \\square & \\\\ \\hline \\square - \\square & \\\\ \\hline 10.0 - 10.9 & \\\\ \\hline 11.0 - 11.9 & \\\\ \\hline \\square - \\square & \\\\ \\hline \\square - \\square & \\\\ \\hline & 20 \\end{array}$$

Explanation:

Determine class width and limits

Using the Class Limits and Class Width knowledge points

The first class is given as \(7.0 - 7.9\).
The lower class limit of the first class is \(7.0\), and the upper class limit is \(7.9\).
The class width is the difference between consecutive lower class limits:

$$ \text{Class Width} = 8.0 - 7.0 = 1.0 $$

Using this width, we construct the consecutive classes:

• Class 1: \(7.0 - 7.9\)
• Class 2: \(8.0 - 8.9\)
• Class 3: \(9.0 - 9.9\)
• Class 4: \(10.0 - 10.9\)
• Class 5: \(11.0 - 11.9\)
• Class 6: \(12.0 - 12.9\)
• Class 7: \(13.0 - 13.9\)

Sort the data values

Using the Frequency Distribution knowledge point

We sort the 20 given data points in ascending order:

$$ 7.2, 7.2, 7.7, 7.9, 8.1, 8.1, 8.5, 8.8, 9.1, 9.1, 9.6, 10.1, 10.6, 11.3, 11.4, 11.7, 12.2, 12.5, 13.1, 13.7 $$

Count frequencies for each class

Using the Frequency Distribution knowledge point

We count how many data points fall into each class interval:

• For \(7.0 - 7.9\): \(7.2, 7.2, 7.7, 7.9\) \(

ightarrow 4\) cities

• For \(8.0 - 8.9\): \(8.1, 8.1, 8.5, 8.8\) \(

ightarrow 4\) cities

• For \(9.0 - 9.9\): \(9.1, 9.1, 9.6\) \(

ightarrow 3\) cities

• For \(10.0 - 10.9\): \(10.1, 10.6\) \(

ightarrow 2\) cities

• For \(11.0 - 11.9\): \(11.3, 11.4, 11.7\) \(

ightarrow 3\) cities

• For \(12.0 - 12.9\): \(12.2, 12.5\) \(

ightarrow 2\) cities

• For \(13.0 - 13.9\): \(13.1, 13.7\) \(

ightarrow 2\) cities

Total sum check: \(4 + 4 + 3 + 2 + 3 + 2 + 2 = 20\).

Answer:

Population (millions of people)	Number of Cities
\(8.0 - 8.9\)	\(4\)
\(9.0 - 9.9\)	\(3\)
\(10.0 - 10.9\)	\(2\)
\(11.0 - 11.9\)	\(3\)
\(12.0 - 12.9\)	\(2\)
\(13.0 - 13.9\)	\(2\)