Answer
Mean = 20.56
Median = 24.4
Standard deviation = 7.7420
Step-by-step explanation
Mean
The mean is the average of the distribution. It is obtained mathematically as the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
Σx = Sum of the variables
N = number of variables
Σx = 24.4 + 5.6 + 25.4 + 26.7 + 20.7 = 102.8
N = 5
Mean = (Σx)/N
Mean = (102.8/5) = 20.56
Median
The median is the variable that falls in the middle of the distribution when all the variables are arranged either in ascending or descending order.
So, to obtain the median for this, we have to arrange all the values in data.
24.4, 5.6, 25.4, 26.7, 20.7
Rearranging in ascending order,
5.6, 20.7, 24.4, 25.4, 26.7
Since there are 5 variables here, we can see that the median is the number in the middle, that is, the third number,
Median = 24.4
Standard deviation
Standard deviation expresses how far most of the variables are, from the mean. It is mathematically given as,
Standard deviation = σ = √[Σ(x - xbar)²/N]
x = each variable
xbar = mean
N = number of variables
Σ(x - xbar)² = (24.4 - 20.56)² + (5.6 - 20.56)² + (25.4 - 20.56)² + (26.7 - 20.56)² + (20.7 - 20.56)²
Σ(x - xbar)² = (3.84)² + (-14.96)² + (4.84)² + (6.14)² + (0.14)²
Σ(x - xbar)² = 14.7456 + 223.8016 + 23.4256 + 37.6996 + 0.0196
Σ(x - xbar)² = 299.692
N = 5
Standard deviation = σ = √[Σ(x - xbar)²/N]
Standard deviation = σ = √[299.692/5] = 7.7420
Hope this Helps!!!