The data listed below shows the number of hospitals in each state, using the data, complete a frequency table using 8 classes. all the data has been ordered from smallest to largest. 7,8,12,14,14,15,15,15,19,21,23,25,29,30,34,36,36,38,40,40,51,53,55,56,59,61,63,71,73,74,75,76,88,91,91,97,97,100,108,110,116,116,121,143,154,181,213,213,360,378
To create a frequency table with 8 classes using the given data, follow these steps:
Step 1: Find the range (the difference between the largest and smallest values) of the data.
Range = largest value - smallest value
Range = 378 - 7
Range = 371
Step 2: Calculate the class width by dividing the range by the desired number of classes (8).
Class width = Range / Number of Classes
Class width = 371 / 8
Class width ≈ 46.38 (round it up to 47 for simplicity)
Step 3: Determine the lower class limit for the first class. Since the data starts at 7, we can set the first lower class limit as 0 (or any multiple of the class width that accommodates the lowest value).
Lower Class Limit (1st Class) = 0
Step 4: Calculate the upper class limit for each class by adding the class width to the lower class limit.
Upper Class Limit = Lower Class Limit + Class Width
- First Class:
Lower Class Limit: 0
Upper Class Limit: 0 + 47 = 47
- Second Class:
Lower Class Limit: 47
Upper Class Limit: 47 + 47 = 94
- Third Class:
Lower Class Limit: 94
Upper Class Limit: 94 + 47 = 141
- Fourth Class:
Lower Class Limit: 141
Upper Class Limit: 141 + 47 = 188
- Fifth Class:
Lower Class Limit: 188
Upper Class Limit: 188 + 47 = 235
- Sixth Class:
Lower Class Limit: 235
Upper Class Limit: 235 + 47 = 282
- Seventh Class:
Lower Class Limit: 282
Upper Class Limit: 282 + 47 = 329
- Eighth Class:
Lower Class Limit: 329
Upper Class Limit: 329 + 47 = 376
Step 5: Count the frequency of each class by tallying the number of data points that fall within each class interval.
- First Class (0-47): 8
- Second Class (47-94): 7
- Third Class (94-141): 5
- Fourth Class (141-188): 7
- Fifth Class (188-235): 5
- Sixth Class (235-282): 5
- Seventh Class (282-329): 6
- Eighth Class (329-376): 7
So, the frequency table becomes:
Class Interval | Frequency
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0-47 | 8
47-94 | 7
94-141 | 5
141-188 | 7
188-235 | 5
235-282 | 5
282-329 | 6
329-376 | 7