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Skip in 10
To determine how the original correlation coefficient \( r \) is affected after removing the inaccurate data points, let's follow these steps: ### Given Data: - Number of observations, \( n = 11 \) - Mean of \( x \), \( \bar{x} = 7 \) - Standard deviation of \( x \), \( \sigma_x = 2 \) - Mean of \( y \), \( \bar{y} = \bar{y} \) (same as original mean, denoted as \( \bar{y} \)) - Standard deviation of \( y \), \( \sigma_y = 4 \) - Correlation coefficient, \( r = 0.5 \) - Inaccurate data points to be removed: \( x = -7 \), \( y = -9 \) ### Step 1: Calculate the Sums Before Removal 1. Sum of \( x \): \[ \sum x = n \times \bar{x} = 11 \times 7 = 77 \] 2. Sum of \( y \): \[ \sum y = n \times \bar{y} = 11 \times \bar{y} \] 3. Sum of \( xy \): The correlation coefficient formula is: \[ r = \frac{\sum xy - n \bar{x} \bar{y}}{(n-1) \sigma_x \sigma_y} \] Rearranging to find \( \sum xy \): \[ \sum xy = r (n-1) \sigma_x \sigma_y + n \bar{x} \bar{y}
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Related Questions
In a state with a total population of 70,000 adults, 34, 000 are males and out of a total of 5000 graduates, 700 are females. Out of 1200 graduate employees of the state 200 are females. Is there any sex bias in education among people? The state holds that no distribution is made in appointments with respect of sex. How far this claim is substantiated by the data given above? Find the equation of best fitted suitable curve of the form y = aebx for the following data: In a very hotly fought battle atleast 70% of the combatants lost an eye, atleast 75% lost an ear, atleast 80% lost an arm and atleast 85% lost a leg. How many atleast must have lost all four? 
