Questions: A chemical technician measured the temperatures (in °C) of 18 different solutions. The temperatures are shown below. Complete the grouped relative frequency distribution for the data. (Note that we are using a class width of 6.) Write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage. Temperature (in °C): 118, 102, 115, 108, 98, 107, 110, 109, 117, 97, 116, 113, 115, 95, 100, 106, 104, 109 Temperature (in °C) Relative frequency 95 to 100 □ 101 to 106 □ 107 to 112 □ 113 to 118 □

A chemical technician measured the temperatures (in °C) of 18 different solutions. The temperatures are shown below.
Complete the grouped relative frequency distribution for the data. (Note that we are using a class width of 6.)
Write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage.

Temperature (in °C):
118, 102, 115, 108, 98, 107, 110, 109, 117, 97, 116, 113, 115, 95, 100, 106, 104, 109

Temperature (in °C) Relative frequency
95 to 100 □
101 to 106 □
107 to 112 □
113 to 118 □

Transcript text: A chemical technician measured the temperatures (in ${ }^{\circ} \mathrm{C}$ ) of 18 different solutions. The temperatures are shown below. Complete the grouped relative frequency distribution for the data. (Note that we are using a class width of 6 .) Write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage. \begin{tabular}{|lllll|} \hline \multicolumn{5}{c|}{\begin{tabular}{c} Temperature \\ (in $\left.{ }^{\circ} \mathrm{C}\right)$ \end{tabular}} \\ \hline 118 & 102 & 115 & 108 & 98 \\ 107 & 110 & 109 & 117 & 97 \\ 116 & 113 & 115 & 95 & 100 \\ 106 & 104 & 109 & & \\ \hline \end{tabular} \begin{tabular}{|cc|} \hline \begin{tabular}{c} Temperature \\ (in ${ }^{\circ} \mathrm{C}$ ) \end{tabular} & \begin{tabular}{c} Relative \\ frequency \end{tabular} \\ \hline 95 to 100 & $\square$ \\ 101 to 106 & $\square$ \\ 107 to 112 & $\square$ \\ 113 to 118 & $\square$ \\ \hline \end{tabular}

Solution

Solution Steps

To complete the grouped relative frequency distribution, we first need to count how many temperatures fall within each specified range (class). Then, we calculate the relative frequency for each class by dividing the count of temperatures in that class by the total number of temperatures. Finally, we round each relative frequency to the nearest hundredth.

Step 1: Count Temperatures in Each Class

We categorize the temperatures into the specified ranges:

For the range $95$ to $100$: The temperatures $95, 98, 97, 100$ fall within this range. Thus, the count is $4$.
For the range $101$ to $106$: The temperatures $102, 105, 106$ fall within this range. Thus, the count is $3$.
For the range $107$ to $112$: The temperatures $107, 110, 109$ fall within this range. Thus, the count is $5$.
For the range $113$ to $118$: The temperatures $115, 115, 116, 113, 118$ fall within this range. Thus, the count is $6$.

Step 2: Calculate Relative Frequencies

Next, we calculate the relative frequency for each class by dividing the count of temperatures in that class by the total number of temperatures, which is $18$:

For the range $95$ to $100$: \[ \text{Relative Frequency} = \frac{4}{18} \approx 0.22 \]
For the range $101$ to $106$: \[ \text{Relative Frequency} = \frac{3}{18} \approx 0.17 \]
For the range $107$ to $112$: \[ \text{Relative Frequency} = \frac{5}{18} \approx 0.28 \]
For the range $113$ to $118$: \[ \text{Relative Frequency} = \frac{6}{18} \approx 0.33 \]

Final Answer

The completed grouped relative frequency distribution is as follows:

$95$ to $100$: $0.22$
$101$ to $106$: $0.17$
$107$ to $112$: $0.28$
$113$ to $118$: $0.33$

Thus, the final answer is: \[ \boxed{ \begin{array}{|c|c|} \hline \text{Temperature Range} & \text{Relative Frequency} \\ \hline 95 \text{ to } 100 & 0.22 \\ 101 \text{ to } 106 & 0.17 \\ 107 \text{ to } 112 & 0.28 \\ 113 \text{ to } 118 & 0.33 \\ \hline \end{array} } \]

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