Answer:
Mean = 52.09
The range is 88
Variance = 433. 44
Standard Deviation= s= 20.82
Step-by-step explanation:
The mean is obtained by adding all the values and dividing the number values .
Mean = 37+ 8 +65+ 76 +21 +96+ 46 +19 +75+ 72+ 58+ 84/12
Mean = 573/11 = 52.09
The mean gives the average value .
Range is the difference between the highest and smallest value. The highest value is 96 and lowest value is 8
96 - 8 = 88
The range is 88.
The range gives an idea of the spread of values between two points.
The variance can be calculated by
∑x²= 1369+ 64+ 4225+ 5776+ 441+ 9216+ 2116+ 361+ 5625+ 5184+ 3364= 37741
S²= ∑x²/n - ( ∑x/n)²
= ∑37741/ 11 - (52.09)²
= 3431 - 2997.56 = 433. 44
Standard deviation is the square root of the variance
s= √433. 44= 20.82
The large value of standard deviation implies that the observations are scattered widely about the mean. A smaller value indicates that the observations in data set are close to mean.
