Construct both an ungrouped and a grouped frequency distribution for the data given below:
207 211 204 208 202 203 211 202 205 212
210 212 204 199 204 201 213 200 204 207
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Ungrouped means getting the frequency of each score, while grouped means you combine the frequency of adjacent scores.
To construct both an ungrouped and a grouped frequency distribution, we need to first organize the data in ascending order.
The given data:
199 200 201 202 202 203 204 204 204 205
207 207 208 210 211 211 212 212 213
1. Ungrouped Frequency Distribution:
This distribution lists each unique value in the dataset along with its frequency, without grouping the data into intervals.
To create an ungrouped frequency distribution, we count the occurrence of each unique value in the dataset. Here is the ungrouped frequency distribution for the given data:
Value Frequency
199 1
200 1
201 1
202 2
203 1
204 3
205 1
207 2
208 1
210 1
211 2
212 2
213 1
2. Grouped Frequency Distribution:
A grouped frequency distribution groups the data into intervals or classes and shows the frequency of occurrence for each interval. To create a grouped frequency distribution, we need to determine the range and the number of intervals.
Range = Maximum value - Minimum value
Range = 213 - 199 = 14
To determine the number of intervals, we can use a rule of thumb such as the "Square Root Rule." The square root of the number of data points (in our case, 19) is approximately 4.36. Since it's not possible to have a decimal number of intervals, we round up to 5 intervals.
Interval width = Range / Number of intervals
Interval width = 14 / 5 = 2.8
To create the grouped frequency distribution, we divide the data into intervals and count the number of values falling into each interval.
Interval Frequency
199-201 3
202-204 6
205-207 3
208-210 2
211-213 5
Note: The intervals are inclusive of the lower bound and exclusive of the upper bound. For example, the interval 199-201 includes values from 199 up to but not including 202.
This is how you construct both an ungrouped and a grouped frequency distribution for the given data.