Let's start with the tablet prices from store A.
$140, $150, $160, $180, $190, $200, $250, $250
For this data set, the greatest value is 250 and the least value is 140.
Range: 250- 140=110
Store B
Now, we can do the same for the prices from store B.
$160, $190, $190, $225, $240, $260, $285, $310
For this data set, the greatest value is 310 and the least value is 160.
Range: 310- 160=150
Standard Deviation
The standard deviation of a set of data is the average amount by which each individual value deviates or differs from the .
Standard Deviation
sqrt((x_1-μ )^2 +(x_2-μ )^2 +... +(x_n-μ )^2/n)
In the above formula, x_1, ... ,x_n are the values of the set of data, μ is the mean, and n is the number of values.
Store A
For this data set, we can calculate the sum of the values.
140+150+160+180+
190+200+250+250
= 1520
The mean is the sum of the values 1520 divided by the number of values 8.
μ= 1520 8=190
Let's use this value and apply the formula to each value in the set.
| x_n
|
x_n-μ
|
(x_n-μ)^2
|
| 140
|
140-190=-50
|
(-50)^2= 2500
|
| 150
|
150-190=-40
|
(-40)^2= 1600
|
| 160
|
160-190=-30
|
(-30)^2= 900
|
| 180
|
180-190=-10
|
(-10)^2= 100
|
| 190
|
190-190=0
|
0^2= 0
|
| 200
|
200-190=10
|
10^2= 100
|
| 250
|
250-190=60
|
60^2= 3600
|
| 250
|
250-190=60
|
60^2= 3600
|
| Sum of Values
|
= 12400
|
Finally, we need to divide by 8 and then calculate the square root.
Standard Deviation: sqrt(12400/8)≈ 39.4
Store B
For this data set, we can calculate the sum of the values.
160+190+190+225+
240+260+285+310
= 1860
The mean is the sum of the values 1860 divided by the number of values 8.
μ= 1860 8=232.5
Let's use this value and apply the formula to each value in the set.
| x_n
|
x_n-μ
|
(x_n-μ)^2
|
| 160
|
160-232.5=-72.5
|
(-72.5)^2= 5256.25
|
| 190
|
190-232.5=-42.5
|
(-42.5)^2=1806.25
|
| 190
|
190-232.5=-42.5
|
(-42.5)^2=1806.25
|
| 225
|
225-232.5=-7.5
|
(-7.5)^2= 56.25
|
| 240
|
240-232.5=7.5
|
7.5^2= 56.25
|
| 260
|
260-232.5=27.5
|
27.5^2= 756.25
|
| 285
|
285-232.5=52.5
|
52.5^2= 2756.25
|
| 310
|
310-232.5=77.5
|
77.5^2= 6006.25
|
| Sum of Values
|
= 18500
|
Finally, we need to divide by 8 and then calculate the square root.
Standard Deviation: sqrt(18500/8)≈ 48.1
Comparison
The range of the tablet prices for Store A is 110, and the range of the prices for Store B is 150. So, the prices are more spread out for Store B. The standard deviation for Store A is about 39.4, and the standard deviation for Store B is about 48.1. Therefore, the typical price for Store A differs by 39.4 from the mean, while the typical price for Store B differs by 48.1.
