For the following sample data: 10, 9, 6, 6, 1, 11, 8, 6, 3, 2, 11, 1, 12, 7, 10, 9.

Calculate:

1) Mean

2) Median

3) Mode

4) Variance + Sum of squares

5) Standard Deviation

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MEAN

total terms=16

Sum=(10+9+6+6+1+11+8+6+3+2+11+1+12+7+10+9)=112

mean=112/16=7

Median

for median arrange data in increasing order

1,1,2,3,6,6,6,7,8,9,9,10,10,11,11,12

(7+8)/2=7.5 median=7.5

Mode

most repeative values are mode=6,6,6

Mode=6

Varience

segma=segma(xi-mean)^2/N

mean=7

(1-7)+(1-7)+(2-7)+(3-7)+(6-7)+(6-7)+(6-7)+(6-7)+(7-7)+(8-7)+()+()+()+()+()

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segma=segma(xi - mean)^2/N

(1-7)^2+(1-7)^2+(2-7)^2+(3-7)^2+(6-7)^2+(6-7)^2+(6-7)^2+(6-7)^2+(7-7)^2+(8-7)^2+(9-7)^2+(10-7)^2+(10-7)^2+(11-7)^2+(11-7)^2+(12-7)^2=200

Standerd deviation =200/7=28.57

=sqrt(28.57)=5.34

Variance

for variance we just need t devide 200 with (N - 1)

N=16

N-1=15

200/15=13.33

S^2=13.33

s=sqrt(13.33)=3.65

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