Question

26. Calculate each value requested for the following set of scores.

a. ΣX X Y

b. ΣY 1 6

c. ΣXΣY 3 0

d. ΣXY 0 –2

2 –4

27. Use summation notation to express each of the following calculations. a. Add 3 points to each score, then find the sum of the resulting values. b. Find the sum of the scores, then add 10 points to the total. c. Subtract 1 point from each score, then square each of the resulting values. Next, find the sum of the squared numbers. Finally, add 5 points to this sum.

28. Describe the relationships between a sample, a population, a statistic and a parameter.

Answer 1

26.

Scores of X: 1,3,0,2 . We define the values of X as X1, X2, X3, X4 respectively. So, X1=1,X2=3,X3=0,X4=2

Scores of Y: 6,0,-2,-4. We define the values of X as Y1,Y2,Y3,Y4 respectively. So, Y1=6,Y2=0,Y3=-2,Y4=-4

a.

XXY = (X1*X1*Y1)+(X2*X2*Y2)+(X3*X3*Y3)+(X4*X4*Y4) = (1*1*6)+(3*3*0)+(0*0*(-2))+(2*2*(-4))

= 6+0+0+(-16) = -10

b.

Y = Y1+Y2+Y3+Y4 = 6+0+(-2)+(-4) = 0

c.

XY = (X1+X2+X3+X4)*(Y1+Y2+Y3+Y4) = (X1+X2+X3+X4)*0 [from previuos result]

= 0

d.

XY = (X1*Y1)+(X2*Y2)+(X3*Y3)+(X4*Y4) = (1*6)+(3*0)+(0*(-2))+(2*(-4)) = 6+0+0+(-8) = -2

27.

Let X be the value of each scores. Let X takes values X1,X2,...,XN. Where N is any positive integer.

a.

(X1+3)+(X2+3)+.....+(XN+3) = (X+3)

b.

X1+X2+.....+XN+10 = ( X) + 10

c.

((X1-1)^2)+((X2-1)^2)+.....+((XN-1)^2)+5 = (((X-1)^2))+5

'*' MEANS MULTIPLICATION & A^B MEANS .

28.

The collection of all the units whose one or more characteristics are to be studied is defined as Population.

A part of the population which is meant to represent the entire population is called a sample.

A statistical measure based on population values is called a parameter. e.g - population mean, population variance, etc.

A statistical measure based on sample values is called a statistic. e.g - sample mean, sample variance, etc.

We use the statistic(s) to infer about the population parameters.

The statistic(s) gives an idea about the nature of the samples & hence the population that corresponds to the sample by inferring about the parameters of the population.

The parameter gives an idea about the nature of the population.