Solutions
Given:
The prices of a group of 6 items are $10, $15, $20, $25, $30, and $35.
Concept Used:
Steps to find the standard deviation,
1. Calculate the mean (average) of the set of numbers.
2. For each number in the set, subtract the mean and square the result.
3. Find the average of the squared differences calculated in step 2.
4. Take the square root of the result from step 3.
Calculation:
Mean = (10 + 15 + 20 + 25 + 30 + 35) / 6 = 22.50
Subtract the mean from each price and square the result:
⇒ (10 - 22.50)2 = 156.25,
⇒ (15 - 22.50)2 = 56.25,
⇒ (20 - 22.50)2 = 6.25,
⇒ (25 - 22.50)2 = 6.25,
⇒ (30 - 22.50)2 = 56.25,
⇒ (35 - 22.50)2 = 156.25
Calculate the sum of the squared differences:
⇒ 156.25 + 56.25 + 6.25 + 6.25 + 56.25 + 156.25 = 437.5
Divide the sum by the number of prices, and take the square root of it:
⇒ √(437.5/6) = √72.92 = 8.53
∴ The standard deviation of their prices is $8.53.