For the data set 7,5,10,11,12 the mean is x, is 9. what is the standard deviation?

SD(σ)=2.91548

Step-by-step explanation:

Definition:

Standard deviation (SD) measures the volatility or variability across a set of data. It is the measure of the spread of numbers in a data set from its mean value and can be represented using the sigma symbol (σ)

To find out SD you must know the value of Mean and Variance.

Mean=sum of values / N (number of values in set)

Mean=7+5+10+11+12/5

Mean=45/5

Mean=9

Variance=((n1- Mean)2 + ... nn- Mean)2) / N-1 (number of values in set - 1)

Variance=((7-9)^2 +(5-9)^2+(10-9)^2+(11-9)^2+(12-9)^2))/5-1

Variance=((-2)^2+(-4)^2+(1)^2+(2)^2+(3)^2)/4

Variance=(4+16+1+4+9)/4

Variance=34/4

Variance=8.5

Standard Deviation(σ)=√Variance

σ = √8.5

By taking the square root of √8.5 we get;

σ = 2.91548

Thus the value of Standard Deviation(σ)=2.91548

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.