Measures of Dispersion- statistics a.pptx
- 1. Measures of Dispersion Dr Binshina Basheer Junior Resident Dept of Community Medicine GMC Kozhikode
- 2. Lets Revise Measures of central tendency ?
- 3. Measures of dispersion: Shows how the data is spread or scattered around the central value
- 4. Measures of Dispersion Absolute measures of Dispersion Standard deviation Mean absolute deviation Range Interquartile range Relative measures of Dispersion Coefficient of variation Coefficient of mean deviation Coefficient of quartile deviation
- 5. Range • Simplest measure of dispersion • Range = X largest – X smallest
- 6. Range Advantages • Simple to calculate • Simple to interpret Disadvantages • Calculated based on extreme values (H&L) • Therefore may not reflect the true variability of the data
- 7. Why Range can be misleading 1. Ignores the way in which data is distributed 2. Sensitive to outliers
- 8. Quartiles • Quartiles split the ranked data into 4 segments with an equal number of values per segment • 9, 5, 7, 13 , 9 , 6 , 5 , 10 , 8 , 9, 12 , 6, 11, 9,5
- 9. Locating Quartiles • Find a quartile by determining the value in the appropriate position in the ranked data, where First quartile(Q1) position: (n+1)/4 Second quartile(Q2) position: (n+1)/2 Third Quartile(Q3) position: (n+1)3/4
- 10. Interquartile Range • IQR = Q3 – Q1 • Measures the spread in the middle 50% of the data • IQR is not influenced by outliers or extreme values
- 11. Mean deviation Advantages • Simple to calculate • Easy to understand • Average of deviations of values from the mean Disadvantage • Ignoring sign is not an acceptable mathematical procedure
- 12. Variance = arithmetic mean x ̄ n = sample size Xi = ith value of variable X • Average of squared deviations of values from the mean
- 13. Standard Deviation • MC used measure of variation • Shows variation about the mean • Root square of the variance • Same units as original data 6A 15 25 30 35 40
- 14. Standard Deviation Advantages • The best measure for variability • Consider all observations for its calculation • Mathematically sound formula Disadvantages • More difficult to calculate • Extreme values will have more influence on std dev
- 16. Measures of dispersion: summary characteristics • The more the data is spread out, the greater the range, variance & SD • The less the data is spread out, the smaller the range, variance & SD • If the values are all the same, range, variance & SD will be zero
- 17. Relative measures of dispersion 1. Coefficient of variation Mean Standard devn Ht in cm 160 16 Wt in kg 60 9 Compare & comment on the variation between Height & weight?
- 18. Relative measures of dispersion 2. Coefficient of range
Editor's Notes
- #2: Measures of central tendency is a central value that the data values group around
- #3: Same centre, different variation Aka measures of variability, measures of spread
- #5: Dataset B is thrice variable than A
- #9: n is the number of observed values
- #11: 9 mins
- #25: 16:57
- #26: Ht & wt have different units , cannot be compared directly To compare their variation we have to convert data into a unit less measure of variance Coefficient of variation