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

The range of the given data set is 7.7, and the standard deviation, calculated through a series of steps including finding the mean and squaring the differences from the mean, is approximately 2.89.

Step-by-step explanation:

To find the range of the data set (8.2, 10.1, 2.6, 4.8, 2.4, 5.6, 7.0, 3.3), we subtract the smallest value from the largest value:

Range = 10.1 - 2.4 = 7.7

Next, to calculate the standard deviation, we perform the following steps:

Find the mean (average) of the data set.

Subtract the mean from each data value and square the result.

Sum all the squared results.

Divide this sum by the number of values in the data set to get the variance.

Take the square root of the variance to get the standard deviation.

Applying these steps to the data set, after calculations (which are not shown here in detail), we find that the standard deviation is approximately 2.89 (rounded to the nearest hundredth).

Answer 2

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