If n1 = 10, n2 = 5 are the sizes of a male and female student group with mean ages x̄1 = 10, x̄2 = 4, respectively, with an equal standard deviation σ1 = σ2 = 1, the standard deviation of the combined series with size n1 + n2 and combined mean x̄ = 8 is equal to:
3
To find the standard deviation of the combined series, we need to calculate the combined variance first. Given:
- n1 = 10 (size of male group)
- n2 = 5 (size of female group)
- x̄1 = 10 (mean age of male group)
- x̄2 = 4 (mean age of female group)
- n = n1 + n2 = 15 (size of combined group)
- x̄ = 8 (combined mean age)
- σ1 = σ2 = 1 (standard deviation of each group)
Variance of each group (σ1² and σ2²) = 1² = 1
The formula for combined variance σ² for two groups is:
σ² = [(n1 * σ1²) + (n2 * σ2²) + (n1 * (x̄1 - x̄)²) + (n2 * (x̄2 - x̄)²)] / nSubstitute the values:
σ² = [(10 * 1) + (5 * 1) + (10 * (10 - 8)²) + (5 * (4 - 8)²)] / 15
= [10 + 5 + 10 * 4 + 5 * 16] / 15
= [15 + 40 + 80] / 15
= 135 / 15
= 9
Thus, the standard deviation σ is:
σ = √9 = 3
The standard deviation of the combined series is 3.
Similar Questions
The following table gives zone wise survey report of the people of a country who take tea. Study the table and answer the question.
The ratio of the total number of people surveyed who take tea more than 3 times a day to the number of people who do not take tea at all is:
The weighted aggregate price index with base year quantities taken as weights is known as:
If X ~ N(5,16), then the first quartile of X is equal to:
β2 of normal distribution is _____.
Which of the following is true?
Important Questions from Statistics
Match the following:
(a) Marginalist Revolution (i) Samuelson (b) Multiplier-Accelerator model (ii) J. R. Hicks (c) IS-LM curves (iii) Jevous (d) Real Business Cycle (iv) Robert J. Borro Choose the correct option from those given below:
Which one of the following responses is true as a solution to simultaneous equation bias?
A. OLS method
B. Principle Component Method
C. Two - stage Least Square Method (2 SLS method)
D. Full Information Maximum Likelihood method (FIML)
Choose the correct option.
Time series under the condition (E xt ) = μ and cov(x t, x t + k ) = Y(K) is said to be
Given the sample size 400 with the sample mean 99, the population mean 100 and computed value of z statistic at 2.5, the value of population standard deviation will be
Which one of the following price index numbers satisfies the factor reversal test?
