Business Mathematics and Basic Statistics · Class 12 Commerce
Ch 7Measures of Dispersion — Class 12 Business Mathematics and Basic Statistics, concept-first.
The measures of central tendency covered earlier — mean, mode, median — each summarise a data set with a single representative value, but they say nothing about how spread out the data is around that value.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Mean Deviation about the Mean
The mean deviation about the mean averages the absolute distances of every observation from the arithmetic mean: for individual data, or for a frequency distribution ().
Most relevant Q&A
- The number of vehicles sold per day by a car dealership over 25 days is distributed as follows. Find the mean deviation about the mean. | Ve…Free
- The daily sales (in ₹ thousand) of a small retail shop over 6 days were: 10, 12, 8, 15, 14, 13. Find the mean deviation about the mean.Free
- In a survey of 50 employees, the number of days absent in a quarter is distributed as follows. Find the mean deviation about the mean. | Day…Free
- The marks obtained by 40 students in an examination are grouped as follows (the same distribution as Worked Example 3 of the Measures of Cen…Free
In previous exams
How often this chapter’s concepts have been examined — real appearance data, never estimated.
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Mean Deviation about the Mean — Discrete Data
The measures of central tendency covered earlier — mean, mode, median — each summarise a data set with a single representative value, but they say nothing about how spread out the data is around that…
Mean Deviation about the Mean — Continuous (Grouped) Data
When the data is grouped into class intervals, the mean deviation about the mean is computed exactly the same way as for a discrete frequency distribution, with one adjustment already familiar from co…
Mean Deviation about the Median — Discrete Data
The mean deviation can equally be measured about the median instead of the mean — averaging the absolute distances of every observation from the middle value of the data set rather than from its arith…
Mean Deviation about the Median — Continuous (Grouped) Data
Extending mean deviation about the median to grouped/continuous data first requires the median of a continuous distribution itself — a construction the measures-of-central-tendency chapter deliberatel…
Variance and Standard Deviation — Direct Method
Mean deviation uses absolute values to stop positive and negative deviations from cancelling out. An alternative, more mathematically convenient way to avoid the cancellation is to square every deviat…
Standard Deviation — Step-Deviation Method
Exactly as with the mean (measures-of-central-tendency chapter), computing directly can involve large, awkward numbers when the class marks themselves are large.
Coefficient of Variation
Standard deviation measures spread in the same units as the original data — rupees, marks, kilograms, whatever the data represents.
Exercises
+−Show 4 questionsHide questions4 questions
- Q11The number of vehicles sold per day by a car dealership over 25 days is distributed as follows. Find the mean deviation about the mean. | Ve…Free
- Q12The weights (in kg) of 60 persons are grouped as follows. Find the median using the interpolation formula, and hence the mean deviation abou…Free
- Q13The number of overtime hours worked by 5 employees in a week is: 4, 8, 6, 5, 7. Find the variance and standard deviation.Preview
- Q14Two batches of light bulbs have the following average life and standard deviation: Batch A: mean $=1000$ hours, SD $=50$ hours; Batch B: mea…Preview
More questions
+−Show 10 questionsHide questions10 questions
- Example 1The daily sales (in ₹ thousand) of a small retail shop over 6 days were: 10, 12, 8, 15, 14, 13. Find the mean deviation about the mean.Free
- Example 2In a survey of 50 employees, the number of days absent in a quarter is distributed as follows. Find the mean deviation about the mean. | Day…Free
- Example 3The marks obtained by 40 students in an examination are grouped as follows (the same distribution as Worked Example 3 of the Measures of Cen…Free
- Example 4The ages (in years) of 5 employees in a small firm are 22, 25, 19, 30, 28. Find the mean deviation about the median.Preview
- Example 5The number of customer complaints received per day by a company, recorded over 40 days, is given below. Find the mean deviation about the me…Preview
- Example 6The marks of 50 students in an examination are grouped as follows. Find (a) the median using the interpolation formula, and (b) the mean dev…Preview
- Example 7The number of defective items produced per hour by a machine, recorded over 20 hours, is given below. Find the variance and standard deviati…Preview
- Example 8The marks of 40 students, grouped as in Worked Example 3 (mean $=27$), are given below. Find the variance and standard deviation using the d…Preview
- Example 9Using the same marks distribution as Worked Example 8, find the standard deviation by the step-deviation method (taking $A=25$, $h=10$), and…Preview
- Example 10The monthly returns (in %) of two mutual funds over the past year have the following mean and standard deviation: Fund A: mean $=12\%$, SD $…Preview