Range 1.1 and coeeficient of variance.

Define range, and variance in simple way.

1. The difference between the largest and smallest value of data set is called range. It is the simplest measure of spread. Range (R) = Largest value (L) – Smallest Value (S) Weight of students: 55, 89, 65, 74, 79, 98, 89, 68 Range = 98 - 55 = 43 Range Largest Value Smallest Value While range is having limited use as a measure of spread. It act as check of the upper and lower limits of data, and if any variable had crossed that limit. Example: if the range of a data of age of school student's is 24, that shall indicate a mistake.

2. Range of grouped data (Discrete Series) Ignore Frequency and calculate range for variable like individual series. Largest value = 10, Lowest value = 5 Range = L - S = 10 - 5 = 5

3. Range of grouped data (Continuous Series) Ignore Frequency and calculate range for variable like individual series. L argest value = Upper limit of highest class (in this case 30-35). S mallest value = Lower limit of lowest class (in this case 5- 10). Range = L - S = 35 - 5 = 30

4. Limitation of range We cant draw any inference of population range form the range of the sample. Range is based on two extreme observations. It gives no weight to the central values of the data . Hence it’s a poor measure of dispersion Group A: 25, 26, 27, 29, 75 Group B: 25, 55, 45, 60, 75 Range for both groups is 50 (75-25) still its clearly visible that B is having higher dispersion.

5. Limitation of range Due to this limitation’s range doesn’t enjoy any prominent place in statistical analysis, still it’s useful is quality control. R ange is used to maintain the quality of products produced in factories. The quality of products need’s kept within a certain range of values . Which is considered to accepted range. .

6. Coefficient of Range This is a relative measure of dispersion and is based on the value of the range . Coefficient of Range = L = Largest values S= Smallest Value L- S L+S

7. Coefficient of Range Example: Weight of students: 55, 89, 65, 74, 79, 98, 89, 68 Smallest Value Largest Value Coefficient of Range = 98 - 55 98 +55 Coefficient of Range = L- S L+S 43 153 = = 0.28 Why Coefficient?

8. . Coefficient of Range Range (Term A) = 30-15 = 15 Range (Term B) = 88-65 = 23 We can conclude that marks for term B are more diverse, since range is higher. Will coefficient help? Because the base is not same. Can Coefficient help

9. . Will coefficient help? Coefficient of range = L- S L+S = Coefficient of range (Term A) 30-15 30+15 15 45 = = 0.33 Now we get the right picture that Term A is more diverse. Good Job!! Coefficient of Range Coefficient of range (Term B) 88-65 88+65 23 153 = = 0.15 =

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