Question

A store manager is looking at past jewelry sales to determine what sizes of rings to keep in stock. The list shows the ring sizes purchased by the last ten jewelry customers. 9, 7, 6.5, 7.5, 7, 8, 5, 6, 7.5, 8 What is the variance of the data? Round to the nearest hundredths.
0.40
0.72
1.15
2.14

Answer 1

Mean: ( 9 + 7 + 6.5 + 7.5 + 7 + 8 + 5 + 6 + 7.5 + 8 ) : 10 = 7.15
Variance:
(Sigma)² = ( 1.85² + 0.15² + 0.65² + 0.35² + 0.15² + 0.85² + 2.15² + 1.15² + 0.35² + 0.85² ) : 10 ≈ 1.15
Answer: C ) 1.15

Answer 2

We have that

set of data $[9, 7, 6.5, 7.5, 7, 8, 5, 6, 7.5, 8]$

 step 1

Find the mean

$[9+ 7+ 6.5+ 7.5+ 7+ 8+ 5+ 6+ 7.5+ 8]/10 \\ =71.5/10 \\= 7.15$

 step 2

 for each number: subtract the Mean and square the result

$(9-7.15) ^{2} =3.4225 \\ (9-7.15) ^{2} =3.4225 \\ (7-7.15)^{2} = 0.0225 \\ (6.5-7.15)^{2} = 0.4225 \\ (7.5-7.15)^{2} = 0.1225 \\ (7-7.15)^{2} = 0.0225 \\ (8-7.15)^{2} = 0.7225 \\ (5-7.15)^{2} = 4.6225 \\ (6-7.15)^{2} = 1.3225 \\ (7.5-7.15)^{2} = 0.1225 \\ (8-7.15)^{2} = 0.7225$

$Sum=11.525$

 step 3

 work out the mean of those squared differences

$11.525/10 \\ =1.15$

this value is called the "Variance"

the answer is the option

$1.15$