Answer
Number of data that lie within 1 standard deviation of the mean = 4
Step-by-step explanation
To answer this, we need to find the mean and the standard deviation of this distribution first.
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 = 63 + 69 + 58 + 69 + 70 + 58 + 68 = 455
N = 7
Mean = (Σx)/N
Mean = (455/7) = 65
Standard deviation = σ = √[Σ(x - xbar)²/N]
x = each variable
xbar = mean
N = number of variables
Σ(x - xbar)² = (63 - 65)² + (69 - 65)² + (58 - 65)² + (69 - 65)² + (70 - 65)² + (58 - 65)² + (68 - 65)²
Σ(x - xbar)² = (-2)² + (4)² + (-7)² + (4)² + (5)² + (-7)² + (3)²
Σ(x - xbar)² = 4 + 16 + 49 + 16 + 25 + 49 + 9 = 168
N = 7
Standard deviation = σ = √[168/7] = √(24) = 4.90
To now find the data that lie within 1 standard deviation of the mean, we need to find the range that is within 1 standard deviation of the mean first.
Mean = 65
Standard deviation = 4.90
Lower limit = Mean - Standard deviation = 65 - 4.90 = 60.1
Upper limit = Mean + Standard deviation = 65 + 4.90 = 69.9
So, the range that is within 1 standard deviation of the mean = 60.1 to 69.9
The data that lie in this range include {63, 69, 69, 68}
Number of data that lie within 1 standard deviation of the mean = 4
Hope this Helps!!!