Let the data 70, 46, 83, 25, 54, 20, 30, 29, 80 represent the retail prices in rupees of a certain commodity in 9 randomly selected shops in a particular city. What will be the sample variannce of the retail prices, if 1 rupees is added to all the retail prices. (Correct to 2 decimal place accuracy)
Answers
Answer:
49.55
Step-by-step explanation:
add all the no with 1 and divide the sum total by 9
Given:
given data represents the price of commodity in 9 different shops i.e.
70, 46, 83, 25, 54, 20, 30, 29, 80,
To find:
What will be the sample variance of the retail prices, if 1 rupees is added to all the retail prices.
solution:
Sample variance:
Sample variance (s2) is a measure of the degree to which the numbers in a list are spread out. If the numbers in a list are all close to the expected values, the variance will be small. If they are far away, the variance will be large. Sample variance is given by the equation.
It is represented by S² = ∑ (x − x̅)2 / (n − 1)
As 1 rupee is added in each data so new data will become :
71, 47, 84, 26, 55, 21, 31, 30, 81
Now find the mean of the above data:
x̅ = (71+ 47+ 84+ 26+ 55+ 21+ 31+ 30+ 81)/9
=49.55
Now draw the table representing x, (x − x̅),(x − x̅)²
x (x − x̅) (x − x̅)²
71 21.45 460.10
47 -2.55 6.50
84 34.45 1186.80
26 -23.55 554.60
55 5.45 29.70
21 -28.55 815.10
31 -18.55 344.10
30 -19.55 382.20
81 31.45 989.10
∑ (x − x̅)²/(9-1)=4768.2/8
= 596.02
Hence the sample variance of the new data is 596.02