Measures of variability and range for ungrouped data
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The document discusses three measures of variability: range, interquartile range, and measures of central tendency. Range is defined as the difference between the highest and lowest values in a data set. Interquartile range measures the dispersion of the central 50% of values and is calculated by subtracting the lower quartile from the upper quartile. Measures of central tendency, such as the mean and median, measure the average distance of each observation from the center of the distribution and indicate the homogeneity or heterogeneity of a group.
Measures of variability and range for ungrouped data
- 1. ELAINE ELEPANO ANNALYN ESCOBIA MICCAELA DIAZ SAMANTHA MANRILLA
- 2. ARE MEASURES OF THE AVERAGE DISTANCE OF EACH OBSERVATION FROM THE CENTER OF THE DISTRIBUTION. THEY MEASURE THE HOMOGENEITY OF HETEROGENEITY OF A PARTICULAR GROUP.
- 3. DIFFERENCE BETWEEN THE HIGHEST AND THE LOWEST VALUES. THIS IS THE SIMPLEST BUT THE MOST UNRELIABLE MEASURE OF VARIABILITY SINCE IT USES ONLY TWO VALUES IN THE DISTRIBUTION. FORMULA FOR FINDING THE RANGE IS SHOWN BELOW: R = Hv – Lv Where, R = range Hv = highest value Lv = lowest value
- 4. THE HIGHEST COURSEWORK MARK WAS 48 AND THE LOWEST WAS 27 GIVING A RANGE OF 21. IN THE EXAMINATIONTHE HIGHEST MARK WAS 47 AND THE LOWEST 12 PRODUCING A RANGE OF 35. THIS INDICATES THAT THERE WAS WIDER VARIATION IN THE STUDENTS’ PERFORMANCE IN THE EXAMINATION THAN IN THE COURSEWORK.
- 5. A MEASURE THAT INDICATES THE EXTENT TO WHICH THE CENTRAL 50% OF VALUES WITHIN THE DATA SET ARE DISPERSED. IT IS BASED UPON, AND RELATED TO, THE MEDIAN. IN THE SAME WAY THAT THE MEDIAN DIVIDES A DATA SET INTO TWO HALVES, IT CAN BE FURTHER DIVIDED INTO QUARTERS BY IDENTIFYING THE UPPER AND LOWER QUARTILES. THE INTER – QUARTILE RANGE IS FOUND BY SUBTRACTING THE LOWER QUARTILE FROM THE UPPER QUARTILE. FORMULA FOR INTER – QUARTILE RANGE: Q1 – Q2/ 2
- 6. THE EXAMINATION MARKS FOR 20 STUDENTS FOLLOWING A PARTICULAR MODULE ARE ARRANGED IN ORDER OF MAGNITUDE. The median lies at the mid- point between the two central values = half-way between 60 and 62 = 61 The lower quartile lies at the midpoint between the 5th and the 6th values = half- way between 52 and 53 = 52.5 The upper quartile lies at the midpoint between the 15th and 16th values = half- way between 70 and 71 = 70.5 THE INTER – QUART ILE RANGE FOR THIS DATA SET IS THEREFORE: