Answer:
a) Range = 7.7
b) Standard deviation = 2.78
Step-by-step explanation:
Find (a) the range and (b) the standard deviation of the data set 8.2, 10.1, 2.6, 4.8, 2.4,5.6, 7.0,3.3 Round to the nearest hundredth if necessary
We are rearrange the given data:
2.4, 2.6, 3.3, 4.8, 5.6, 7.0, 8.2, 10.1
a) Range
This is calculated as: Highest value - Lowest value
Highest value = 10.1
Lowest value = 2.4
Range = 10.1 - 2.4
= 7.7
b) Standard deviation
Step 1
We find the mean
= Sum of values/ Number of value
= 2.4 + 2.6+ 3.3+ 4.8+ 5.6+7.0+8.2+10.1/8
= 44/8
= 5.5
The formula for standard deviation
= √(x - mean)²/n - 1
= √((2.4 - 5.5)² +( 2.6 - 5.5)²+ (3.3 - 5.5)²+ (4.8-5.5)²+ (5.6 - 5.5)²+(7.0-5.5)² +(8.2 - 5.5)² +(10.1-5.5)2)/8 - 1
= √54.06/7
= √7.722857143
= 2.779002904
approximately = 2.78
