Answer:a. We can use the range approximation formula to estimate the value of s for this set:
s ≈ (range) / 4
To find the range, we subtract the smallest value from the largest value in the set:
range = max - min = 6 - 1 = 5
So, s ≈ (5) / 4 = 1.25.
b. To find the standard deviation s of this data set, we first need to calculate its mean (average):
mean = sum of values / number of values = (5+2+3+6+1+2+4+5+1+3) / 10 = 32 /10 =3.2
Next, we need to calculate each deviation from this mean and square them:
(5-3.2)^2 + (2-3.2)^2 + ... + (3-3.2)^2 = (-0.8)^2 + (-1)^2 + ... +(0.8^")^"
= [(-0.64) ]+[(-1)]+[(-0,49)]+[...]+[(0,64)] ≈ [(0)+(1)+(0)+(7)+(+9)] =17
Then divide by n−1 and take a square root: s= sqrt[17/(10−1)] =sqrt(17/9) ≈sqrt(1,89) ≈±~ ±~** <font color="red"></font>\mathbf{+-}\textbf{\color{red}}* \mathbf{~}\textbf{\color{red}}* \approx ±\mathbf{}\textbf{\color{red}}\sqrt{\mathbf{}.}\text{}[16%]
Therefore, the standard deviation of this data set is approximately ±1.36.
c. Here is a dotplot of the data set:
0 |
|
|
|
|
-+-----+--
1 2 3 4 5 6
The data does not appear to be mound-shaped; rather, it seems skewed to the right.
d. Yes, we can use Chebyshev's theorem to describe this data set because it applies to any distribution, regardless of its shape or symmetry. According to Chebyshev's theorem at least
(1 - (1/k^2)) *100 %
of the measurements lie within k standard deviations from the mean for any value of k greater than one. Using Chebyshev's inequality with k=2 gives us:
At least [1-(1/2²)]*100% =75% of the measurements are within two standard deviations of the mean.
e. We cannot use Empirical Rule to describe this dataset as it only applies when there is a normal distribution present in our dataset with known mean and known variance or Standard Deviation that fulfills certain criteria such as being symmetric and having no outliers which might affect our results significantly if present in large numbers. However, based on our dot plot we see that there is skewness and presence of outliers so Empirical rule won't hold true here
Explanation: