Find the Number of Solutions Discrete
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Discrete And Grouped Data
Data may be discrete or continuous. Discrete data can only take particular values (usually whole numbers) such as the number of children per family. Continuous data can take any value in a given range, for example mass, height, age and temperature.
Sometimes, the collected data can be too numerous to be meaningful. We need to organize data in some logical manner in order to make sense out of them. We could group data into classes. Each class is known as a class interval.
Example:
The data below shows the mass of 40 students in a class. The measurement is to the nearest kg.
| 55 | 70 | 57 | 73 | 55 | 59 | 64 | 72 |
| 60 | 48 | 58 | 54 | 69 | 51 | 63 | 78 |
| 75 | 64 | 65 | 57 | 71 | 78 | 76 | 62 |
| 49 | 66 | 62 | 76 | 61 | 63 | 63 | 76 |
| 52 | 76 | 71 | 61 | 53 | 56 | 67 | 71 |
Construct a frequency table for the data using an appropriate scale.
Solution:
Step 1: Find the range.
The range of a set of numbers is the difference between the least number and the greatest number in the set.
In this example, the greatest mass is 78 and the smallest mass is 48. The range of the masses is then 78 – 48 = 30. The scale of the frequency table must contain the range of masses.
Step 2: Find the intervals
The intervals separate the scale into equal parts.
We could choose intervals of 5. We then begin the scale with 45 and end with 79
Step 3: Draw the frequency table using the selected scale and intervals.
| Mass (kg) | Frequency |
|---|---|
| 45 – 49 | 2 |
| 50 – 54 | 4 |
| 55 – 59 | 7 |
| 60 – 64 | 10 |
| 65 – 69 | 4 |
| 70 – 74 | 6 |
| 75 – 79 | 7 |
Defining Class Intervals For A Frequency Table Or Histogram
Example:
Suppose that we have collected weights from 100 male subjects as part of a nutrition study. For our weight data, we have values ranging from a low of 121 pounds to a high of 263 pounds, giving a total span of 263 - 121 = 142.
Determine reasonable class intervals for a frequency table.
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Median And Quartiles And Percentiles From A Grouped Frequency Table
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Find the Number of Solutions Discrete
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