Answer :
Final answer:
The given dataset's statistics are: mean ≈ 37.43, median = 40, mode is absent, range = 66, variance ≈ 504.88, and standard deviation ≈ 22.47.
Explanation:
let's calculate the requested statistics for the given data
Given data: x = 11, 22, 40, 77, 30, 44, 56
a) Mean:
Mean = (Sum of all values) / (Number of values)
Mean = (11 + 22 + 40 + 77 + 30 + 44 + 56) / 7
Mean ≈ 37.43
b) Median:
To find the median, we first need to arrange the data in ascending order: 11, 22, 30, 40, 44, 56, 77.
Since there are 7 data points, the median will be the value at the (n+1)/2 position, which is the 4th position in this case.
Median = 40
c) Mode:
The mode is the value that appears most frequently in the dataset.
In this case, there is no value that appears more than once, so there is no mode.
d) Range:
Range = Maximum value - Minimum value
Range = 77 - 11
Range = 66
e) Variance:
Variance = Σ((xi - μ)²) / N
Where xi is each data point, μ is the mean, and N is the number of data points.
Variance = ((11 - 37.43)² + (22 - 37.43)² + (40 - 37.43)² + (77 - 37.43)² + (30 - 37.43)² + (44 - 37.43)² + (56 - 37.43)²) / 7
Variance ≈ 504.88
f) Standard Deviation:
Standard Deviation = √Variance
Standard Deviation ≈ √504.88
Standard Deviation ≈ 22.47
So, for the given data:
a) Mean ≈ 37.43
b) Median = 40
c) Mode = No mode
d) Range = 66
e) Variance ≈ 504.88
f) Standard Deviation ≈ 22.47
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