Math Problem Statement
Solution
Let's solve the questions displayed in your image:
Question 71:
If mean and coefficient of variation (CV) of the marks of students is 20 and 80, respectively, what will be the variance of them?
Given:
- Mean () = 20
- Coefficient of Variation () = 80
Formula:
Substitute the values:
Now, variance () is:
Answer: (a) 256
Question 72:
A company's past 10 years' average earnings are ₹40 crores. To have the same average earnings for 11 years (including these 10 years), how much earnings must be made by the company in the eleventh year?
Given:
- Average earnings over 10 years = ₹40 crores
- Total earnings over 10 years =
- New total earnings (for 11 years) =
Earnings in the 11th year:
Answer: (a) ₹40 crores
Question 73:
Origin is shifted by 5, then:
- SD (Standard Deviation)
- QD (Quartile Deviation)
- MD (Mean Deviation)
Key Concept: Shifting the origin (adding or subtracting a constant to every data point) does not affect measures of dispersion such as SD, QD, or MD. Only the mean or median shifts.
Answer: (d) None of these
Do you want further clarifications or detailed steps for any part?
Related Questions:
- What is the difference between standard deviation and variance?
- How does a shift in origin affect the mean and median?
- What is the formula for the coefficient of variation and its use?
- Can there be multiple answers to Question 73 if other transformations (like scaling) are involved?
- How do changes in the sample size affect mean and variance calculations?
Tip:
Always distinguish between measures of central tendency (like mean, median) and dispersion (like variance, standard deviation). Changes in origin and scale have different effects on these measures.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistics
Measures of Central Tendency
Measures of Dispersion
Formulas
Coefficient of Variation: CV = (σ / μ) * 100
Variance: σ^2
Average: Sum of observations / Number of observations
Theorems
Effects of shifting origin on dispersion measures
Suitable Grade Level
Undergraduate / Advanced High School
Related Recommendation
Calculate Variance, Standard Deviation, and Coefficient of Variation
Understanding Dispersion: Variance and Coefficient of Variation
Statistical Summary Problem: Calculating Mean, Sample Size, and Variance from Sample Data
Range, Variance, and Coefficient of Variation for Data Sets
Find the Coefficient of Variation for a Data Set Without Rounding