Let the first entire population be -10 0 10 20 30 and second 8 9 10 11 12. Calculate the mean, median, mode range, variance and 0 and also compare they mean.
To calculate the mean, median, mode, range, variance, and compare the means for the given populations, follow these steps:
First Population: -10, 0, 10, 20, 30
Second Population: 8, 9, 10, 11, 12
Mean:
Mean of the first population: (-10 + 0 + 10 + 20 + 30) / 5 = 10
Mean of the second population: (8 + 9 + 10 + 11 + 12) / 5 = 10
Median:
Median of the first population: 10
Median of the second population: 10
Mode:
Mode of the first population: No mode; there are no values that appear more than once
Mode of the second population: 10
Range:
Range of the first population: 30 - (-10) = 40
Range of the second population: 12 - 8 = 4
Variance:
Variance of the first population:
[(10 - 10)^2 + (0 - 10)^2 + (10 - 10)^2 + (20 - 10)^2 + (30 - 10)^2] / 5
= (0 + 100 + 0 + 100 + 400) / 5 = 120
Variance of the second population:
[(8 - 10)^2 + (9 - 10)^2 + (10 - 10)^2 + (11 - 10)^2 + (12 - 10)^2] / 5
= (4 + 1 + 0 + 1 + 4) / 5 = 2
Comparing the Mean:
The mean is the same for both populations, which is 10.
In summary:
Mean: 10
Median: 10
Mode: 10 (only for the second population)
Range: 40 (first population), 4 (second population)
Variance: 120 (first population), 2 (second population)
Note: The variance is calculated using sample variance formula assuming the populations are samples.