Question
When using descriptive statistics, which measure is best
for understanding data variability?Solution
Standard deviation is the most informative measure of data variability because it quantifies the average deviation of each data point from the mean. By providing insight into the spread of data values around the mean, standard deviation helps analysts understand how clustered or dispersed the data is, which is crucial for interpreting patterns and making comparisons between datasets. Standard deviation is particularly valuable in assessing consistency and identifying outliers, making it essential in descriptive statistical analysis. The other options are incorrect because: • Option 1 (mean) is a central tendency measure, not a measure of variability. • Option 2 (median) indicates the central value but not data spread. • Option 3 (mode) is useful for frequency analysis but not for assessing variability. • Option 5 (range) provides a simple variability measure but lacks the detail of standard deviation, as it only considers extremes.
A class of 30 students appeared in a test. The average score of 12 students is 80, and that of the rest is 75. What is the average score of the class?
- The average of 9 scores is 45. If two new scores are added and their average is 'x', the overall average becomes 20% more than the previous average. Find t...
In an examination the average marks of Rohit is 65. If he got 15 more marks in science and 25 more marks in maths then his average would have been 70. F...
- The average weight of 35 boxes is 24.8 kg. After removing 5 boxes, the average weight becomes 26.1 kg. Find the average weight of the boxes that were remov...
- Find the square of 'x' if the average of 22, 31, 49, 38, 29, and 'x' is 40.
In an examination, Aryan scored 54% marks and passed by 98 marks, while Rohit scored 35% marks and failed by 35 marks. Determine the passing marks for t...
The average score of a class of boys and girls in examination is X. The ratio of boys and girls in the class is 4:3. If the average score of the boys (X...
In a school, the average number of books that some numbers of boys have is 80 and average number of books that some numbers of girls have is 50. If each...
The average of six numbers is 8. When three new numbers are included in such a way that the first number is  twice the second and second number is thri...
Average run scored by a batsman in first ‘x’ matches is 70. In next 12 matches he scored runs with an average of 90 so that his overa...