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Sagot :
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]
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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