Let the first entire population be -10 0 20 30 and second 8 9 10 11 12 calculate the mean,median, mode,range,variance and also compare they mean
To find the mean (average) of a set of numbers, you need to add up all the numbers and divide the sum by the total number of terms.
First set (pop1): -10, 0, 20, 30
Mean (x̄) = (-10 + 0 + 20 + 30) / 4
Mean (x̄) = 40 / 4
Mean (x̄) = 10
Second set (pop2): 8, 9, 10, 11, 12
Mean (ȳ) = (8 + 9 + 10 + 11 + 12) / 5
Mean (ȳ) = 50 / 5
Mean (ȳ) = 10
As you can see, both sets have the same mean of 10.
To find the median, you need to organize the numbers in ascending order and find the middle value (or the average of the two middle values if there is an even number of terms).
First set (pop1): -10, 0, 20, 30
In ascending order: -10, 0, 20, 30
Median: 0
Second set (pop2): 8, 9, 10, 11, 12
In ascending order: 8, 9, 10, 11, 12
Median: 10
The median of the first set is 0, while the median of the second set is 10.
To find the mode, you need to identify the number(s) that appear most frequently in the set.
First set (pop1): -10, 0, 20, 30
Mode: No mode, as none of the numbers repeat.
Second set (pop2): 8, 9, 10, 11, 12
Mode: No mode, as none of the numbers repeat.
Both sets do not have a mode since none of the numbers repeat.
To find the range, subtract the smallest number from the largest number in the set.
First set (pop1): -10, 0, 20, 30
Range: 30 - (-10) = 40
Second set (pop2): 8, 9, 10, 11, 12
Range: 12 - 8 = 4
The range of the first set is 40, while the range of the second set is 4.
To find the variance, you need to calculate the squared deviation of each number from the mean, sum up those squared deviations, and then divide by the total number of terms.
First set (pop1): -10, 0, 20, 30
Variance (σ²) = [((-10 - 10)²) + ((0 - 10)²) + ((20 - 10)²) + ((30 - 10)²)] / 4
Variance (σ²) = [(-20)² + (-10)² + 10² + 20²] / 4
Variance (σ²) = [400 + 100 + 100 + 400] / 4
Variance (σ²) = 1000 / 4
Variance (σ²) = 250
Second set (pop2): 8, 9, 10, 11, 12
Variance (σ²) = [((8 - 10)²) + ((9 - 10)²) + ((10 - 10)²) + ((11 - 10)²) + ((12 - 10)²)] / 5
Variance (σ²) = [(-2)² + (-1)² + 0² + 1² + 2²] / 5
Variance (σ²) = [4 + 1 + 0 + 1 + 4] / 5
Variance (σ²) = 10 / 5
Variance (σ²) = 2
The variance of the first set is 250, while the variance of the second set is 2.
Comparing the mean of both sets, we see that they are equal. However, when comparing the other measures:
- The median of the first set (0) is different from the median of the second set (10).
- Both sets do not have a mode.
- The range of the first set (40) is significantly greater than the range of the second set (4).
- The variance of the first set (250) is larger than the variance of the second set (2).
Overall, while the mean is the same, the other measures (median, mode, range, and variance) vary between the two sets, indicating differences in the distribution and spread of the data.