Complete the table:
Answer:
\begin{tabular}{|c|c|}\hline Class & Class centre \\
\hline 0 - under 5 & $2.5$ \\
5 - under 11 & \\
11 - under 17 & \\
17 - under 23 & \\
23 - under 29 & \\
29 - under 25 & \\
\hline\end{tabular}
Answer (2)
Calculate the class center for the interval 5 - under 11: 2 5 + 11 = 8 .
Calculate the class center for the interval 11 - under 17: 2 11 + 17 = 14 .
Calculate the class center for the interval 17 - under 23: 2 17 + 23 = 20 .
Calculate the class center for the interval 23 - under 29: 2 23 + 29 = 26 .
Calculate the class center for the interval 29 - under 35: 2 29 + 35 = 32 .
The class centers are 8 , 14 , 20 , 26 , 32 .
Explanation
Understanding the Problem We are given a table with class intervals and need to find the corresponding class centers. The class center is the midpoint of each interval. We'll calculate the class center for each given interval using the formula: Class Center = (Lower Bound + Upper Bound) / 2.
Calculating the Class Center (5 - under 11) For the interval 5 - under 11, the lower bound is 5 and the upper bound is 11. Therefore, the class center is calculated as follows: 2 5 + 11 = 2 16 = 8
Calculating the Class Center (11 - under 17) For the interval 11 - under 17, the lower bound is 11 and the upper bound is 17. Therefore, the class center is calculated as follows: 2 11 + 17 = 2 28 = 14
Calculating the Class Center (17 - under 23) For the interval 17 - under 23, the lower bound is 17 and the upper bound is 23. Therefore, the class center is calculated as follows: 2 17 + 23 = 2 40 = 20
Calculating the Class Center (23 - under 29) For the interval 23 - under 29, the lower bound is 23 and the upper bound is 29. Therefore, the class center is calculated as follows: 2 23 + 29 = 2 52 = 26
Calculating the Class Center (29 - under 35) For the interval 29 - under 35, the lower bound is 29 and the upper bound is 35. Therefore, the class center is calculated as follows: 2 29 + 35 = 2 64 = 32
Final Answer The completed table is:
Class
Class centre
0 - under 5
2.5
5 - under 11
8
11 - under 17
14
17 - under 23
20
23 - under 29
26
29 - under 35
32
Examples
Understanding class centers is crucial in statistics for grouped data. For instance, if you're analyzing the ages of people in a town, you might group them into classes like 0-10, 10-20, etc. The class center represents the average age within that group. This helps in estimating overall statistics like the average age of the town's population, providing a practical way to summarize and analyze large datasets.
To calculate the class centers for the given intervals, we find the midpoint using the formula: (Lower Bound + Upper Bound) / 2. The complete table will include class centers of 2.5, 8, 14, 20, 26, and 32 corresponding to each interval. The completed table accurately represents the class centers for each specified range.
;
