Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
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]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
