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Sagot :
a) The approximate mean shipping time: X{bar} = 1.64
b) The approximate variance and standard deviation:
S² = 27.03, σ = 5.2
In this question, we have been given the frequency distribution of shipping times (number of hours between the time an order is placed and the time the order is shipped) for a random sample of 40 orders.
We need to find the approximate mean shipping time, variance and standard deviation.
Number of Hours fi midpoint
4 < 10 8 7
10 < 16 15 13
16 < 22 10 19
22 < 28 7 25
SUM: 40
a) the approximate mean shipping time:
X{bar} = (7.8 + 13.15 + 19.10 + 25.7)/40
X{bar} = 65.75/40
X{bar} = 1.64
b) the approximate variance:
S² = [(7.8 - 1.64)² + (13.15 - 1.64)²+(19.10 - 1.64)²+(25.7 - 1.64)²] / 39
S² = 1054.16/39
S² = 27.03
And the standard deviation:
σ = √S²
σ = √27.03
σ = 5.2
Therefore, for given frequency distribution,
a) mean = 1.64
b) variance = 27.03 and standard deviation = 5.2
Learn more about the mean, standard deviation here:
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