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Use the frequency distribution shown below to construct an expanded frequency distribution.

High Temperatures [tex]$\left( {}^{\circ}F \right)$[/tex]
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline Class & [tex]$17-27$[/tex] & [tex]$28-38$[/tex] & [tex]$39-49$[/tex] & [tex]$50-60$[/tex] & [tex]$61-71$[/tex] & [tex]$72-82$[/tex] & [tex]$83-93$[/tex] \\
\hline Frequency, f & 18 & 43 & 66 & 67 & 84 & 66 & 21 \\
\hline
\end{tabular}

Complete the table below. Round to the nearest hundredth as needed.

High Temperatures [tex]$\left( {}^{\circ}F \right)$[/tex]
\begin{tabular}{|l|c|c|l|l|}
\hline Class & Frequency, f & Midpoint & \begin{tabular}{c}
Relative \\
frequency
\end{tabular} & \begin{tabular}{c}
Cumulative \\
frequency
\end{tabular} \\
\hline [tex]$17-27$[/tex] & 18 & & & \\
\hline [tex]$28-38$[/tex] & 43 & & & \\
\hline [tex]$39-49$[/tex] & 66 & & & \\
\hline [tex]$50-60$[/tex] & 67 & & & \\
\hline [tex]$61-71$[/tex] & 84 & & & \\
\hline [tex]$72-82$[/tex] & 66 & & & \\
\hline [tex]$83-93$[/tex] & 21 & & & \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
Certainly! Let's go through the task step by step:

1. Find the Midpoints of Each Class Interval:
- For the interval [tex]\(17-27\)[/tex], the midpoint [tex]\((17 + 27)/2 = 22.0\)[/tex].
- For the interval [tex]\(28-38\)[/tex], the midpoint [tex]\((28 + 38)/2 = 33.0\)[/tex].
- For the interval [tex]\(39-49\)[/tex], the midpoint [tex]\((39 + 49)/2 = 44.0\)[/tex].
- For the interval [tex]\(50-60\)[/tex], the midpoint [tex]\((50 + 60)/2 = 55.0\)[/tex].
- For the interval [tex]\(61-71\)[/tex], the midpoint [tex]\((61 + 71)/2 = 66.0\)[/tex].
- For the interval [tex]\(72-82\)[/tex], the midpoint [tex]\((72 + 82)/2 = 77.0\)[/tex].
- For the interval [tex]\(83-93\)[/tex], the midpoint [tex]\((83 + 93)/2 = 88.0\)[/tex].

2. Calculate the Total Frequency:
- Total frequency [tex]\(= 18 + 43 + 66 + 67 + 84 + 66 + 21 = 365\)[/tex].

3. Find the Relative Frequencies:
- For the interval [tex]\(17-27\)[/tex], the relative frequency [tex]\(= \frac{18}{365} \approx 0.0493\)[/tex].
- For the interval [tex]\(28-38\)[/tex], the relative frequency [tex]\(= \frac{43}{365} \approx 0.1178\)[/tex].
- For the interval [tex]\(39-49\)[/tex], the relative frequency [tex]\(= \frac{66}{365} \approx 0.1808\)[/tex].
- For the interval [tex]\(50-60\)[/tex], the relative frequency [tex]\(= \frac{67}{365} \approx 0.1836\)[/tex].
- For the interval [tex]\(61-71\)[/tex], the relative frequency [tex]\(= \frac{84}{365} \approx 0.2301\)[/tex].
- For the interval [tex]\(72-82\)[/tex], the relative frequency [tex]\(= \frac{66}{365} \approx 0.1808\)[/tex].
- For the interval [tex]\(83-93\)[/tex], the relative frequency [tex]\(= \frac{21}{365} \approx 0.0575\)[/tex].

4. Calculate the Cumulative Frequencies:
- For the interval [tex]\(17-27\)[/tex], the cumulative frequency [tex]\(= 18\)[/tex].
- For the interval [tex]\(28-38\)[/tex], the cumulative frequency [tex]\(= 18 + 43 = 61\)[/tex].
- For the interval [tex]\(39-49\)[/tex], the cumulative frequency [tex]\(= 61 + 66 = 127\)[/tex].
- For the interval [tex]\(50-60\)[/tex], the cumulative frequency [tex]\(= 127 + 67 = 194\)[/tex].
- For the interval [tex]\(61-71\)[/tex], the cumulative frequency [tex]\(= 194 + 84 = 278\)[/tex].
- For the interval [tex]\(72-82\)[/tex], the cumulative frequency [tex]\(= 278 + 66 = 344\)[/tex].
- For the interval [tex]\(83-93\)[/tex], the cumulative frequency [tex]\(= 344 + 21 = 365\)[/tex].

Now, let’s complete the table with the calculated values:

[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Class} & \text{Frequency, f} & \text{Midpoint} & \text{Relative frequency} & \text{Cumulative frequency} \\ \hline 17-27 & 18 & 22.0 & 0.0493 & 18 \\ \hline 28-38 & 43 & 33.0 & 0.1178 & 61 \\ \hline 39-49 & 66 & 44.0 & 0.1808 & 127 \\ \hline 50-60 & 67 & 55.0 & 0.1836 & 194 \\ \hline 61-71 & 84 & 66.0 & 0.2301 & 278 \\ \hline 72-82 & 66 & 77.0 & 0.1808 & 344 \\ \hline 83-93 & 21 & 88.0 & 0.0575 & 365 \\ \hline \end{array} \][/tex]
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