Answer :
The mean and standard deviation of the given data is 1.5 and 1.58 and when 5 increased to larger value the median does not changed, mean increases and standard deviation decreases.
Given that the expected number of paintings a person will produce over the next 10 days is 0,0,0,1,1,1,2,2,3,5.
(a) To find the mean of the given data firstly add all the terms and then divide the sum by the total numbers count.
mean=∑x/n
Here, ∑x=0+0+0+1+1+1+2+2+3+5=15 and n=10.
Substitute these values in the formula, we get
mean=15/10
mean=1.5
Now, we will find the standard deviation by the formula
σ=√(∑(x-mean)²/(n-1))
So, we have
[tex]\sigma=\sqrt{\frac{(0-1.5)^2+(0-1.5)^2+(0-1.5)^{2}+(1-1.5)^{2}+(1-1.5)^2+(1-1.5)^2+(2-1.5)^2+(2-1.5)^2+(3-1.5)^2+(5-1.5)^2}{10-1}}[/tex]
σ=√(22.5/9)
σ=√2.5
σ=1.58
(b) when 5 is increased to larger value the median remained unchanged, the mean will be increases and the standard deviation will be decreases.
Hence, for the given data the mean and standard deviation when represent the expected number of paintings a person will produce over the next 10 days is 1.5 and 1.58 and when 5 increased to larger value the median does not changed, mean increases and standard deviation decreases.
learn more about the mean and standard deviation from here brainly.com/question/26941429
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