ACTIVITY 3 The following data indicates the scores of 30 students who took the qualifying examination for mathematics challenge. Construct a frequency table. Use a class size of 12 35, 80, 45, 50, 54, 20, 65, 80, 70, 34, 32 90, 95, 70, 24, 11, 70, 65, 70, 45, 32, 70 45, 55, 76, 77, 16, 92, 88, 85
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To construct a frequency table, we need to determine the intervals or classes and count the number of data points that fall into each class. In this case, we'll use a class size of 12. Here's how we can construct the frequency table:
Intervals Frequency
---------------------------
11 - 22 1
23 - 34 1
35 - 46 3
47 - 58 2
59 - 70 8
71 - 82 5
83 - 94 4
95 - 106 2
To create the intervals, we start with the lowest score (11) and add the class size (12) repeatedly until we reach the maximum score of 95. The frequencies represent the number of scores that fall into each interval. For example, there is one score between 11 and 22, three scores between 35 and 46, and eight scores between 59 and 70.
Note: The maximum score of 95 falls into the interval from 95 to 106 to ensure that all the given scores are included in the frequency table.
Answer:
Step-by-step explanation:
Step 1: Sort the data in ascending order:
11, 16, 20, 24, 32, 32, 34, 35, 45, 45, 45, 50, 54, 55, 65, 65, 70, 70, 70, 70, 70, 76, 77, 80, 80, 85, 88, 90, 92, 95
Step 2: Determine the range (difference between the maximum and minimum values):
Range = 95 - 11 = 84
Step 3: Determine the number of classes (bins) and class size:
We are given a class size of 12, so we can calculate the number of classes as:
Number of classes = Range / Class size = 84 / 12 = 7
Step 4: Determine the class intervals:
Since the class size is 12, we can start with the minimum value 11 and create class intervals of width 12. The intervals will be as follows:
11-22, 23-34, 35-46, 47-58, 59-70, 71-82, 83-94
Step 5: Count the frequency of scores within each class interval:
Using the class intervals, we can count the frequency as follows:
11-22: 2
23-34: 3
35-46: 3
47-58: 2
59-70: 6
71-82: 4
83-94: 5
Step 6: Construct the frequency table:
Now, we can create the frequency table using the class intervals and frequencies obtained above:
Class Interval Frequency
11-22 2
23-34 3
35-46 3
47-58 2
59-70 6
71-82 4
83-94 5
This frequency table shows the distribution of scores for the 30 students who took the qualifying examination for the mathematics challenge.