Match the List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| Measure of Dispersion | Property of the Measure of Dispersion | ||
| (A) | Range | (I) | Based on absolute deviation from mean or median |
| (B) | Variance | (II) | Based on squared deviation from mean |
| (C) | Standard Deviation | (III) | Square of standard deviation |
| (D) | Mean Deviation | (IV) | Difference between largest and smallest values |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A-IV, B-III, C-II, D-I
A measure of dispersion tells how widely the values of a data set are spread. Each measure is defined by what it uses: the two extreme values, or the deviations of the values from an average.
(A) Range — this matches (IV) Difference between largest and smallest values. Range \(=L-S\); it uses only the two extreme values.
(B) Variance — this matches (III) Square of standard deviation. Variance is the mean of the squared deviations from the mean, written \(\sigma^2\): it is the square of the standard deviation \(\sigma\).
(C) Standard Deviation — this matches (II) Based on squared deviation from mean. \(\sigma=\sqrt{\frac{\sum(x-\bar{x})^2}{n}}\); the deviations from the mean are squared, averaged and then square-rooted.
(D) Mean Deviation — this matches (I) Based on absolute deviation from mean or median. It is the average of \(|x-A|\), where \(A\) is the mean or the median; the signs of the deviations are ignored.
Note: One item of List-I fits two entries of List-II:
(B) Variance → both (II) and (III). Variance is the mean of the squared deviations from the mean, so it is based on squared deviations (II), and it is also the square of the standard deviation (III).