Final answer:
To find the new mean and standard deviation after removing a wrongly recorded observation, subtract the wrongly recorded value from the original sum and divide by the number of remaining observations. To calculate the new standard deviation, subtract the wrongly recorded value squared from the sum of squared differences and divide by the number of remaining observations.
Step-by-step explanation:
The arithmetic mean of the 200 observations is 70, and the standard deviation is 5. If one of the observations was wrongly recorded, it will affect the mean and standard deviation. To determine the new mean and standard deviation after removing the wrongly recorded observation, we need to find the sum of the remaining 199 observations. Let's call the wrongly recorded observation 'x'. The original sum of the observations is 200 * 70 = 14,000. The sum of the remaining 199 observations is 14,000 - x. Hence, the new arithmetic mean is (14,000 - x) / 199.
To calculate the new standard deviation, we need to find the sum of the squared differences between each observation and the new mean. Let's call the squared differences 'd'. The sum of the squared differences is d + (x - mean)^2. The new standard deviation is the square root of the sum of the squared differences divided by 199.