Question

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

Answer 1

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