A summary of 24 observations of x gave the following information:
∑(x − a) = −73.2 and ∑(x − a)2 = 2115.
The mean of these values of x is 8.95.
(i) Find the value of the constant a.
(ii) Find the standard deviation of these values of x
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To find the value of the constant 'a', we can use the formula for the mean. The sum of the observations (x - a) should equal the number of observations multiplied by the mean. So, we have:
∑(x - a) = n * mean
Plugging in the given values:
-73.2 = 24 * 8.95
Solving this equation, we get:
-73.2 = 214.8
To find the standard deviation, we need to calculate the sum of the squared deviations. The formula for standard deviation is:
standard deviation = √(∑(x - mean)² / n)
Using the given value:
standard deviation = √(2115 / 24)
Calculating this, we find:
standard deviation ≈ 7.9