The following data are the distances between a sample of 20 retail stores and a large distribution center. The distances are in miles.
29; 35; 39; 40; 58; 67; 68; 69; 76; 80; 88; 95; 96; 96; 99; 106; 112; 127; 145; 150
Find the variance and standard deviation (round each to the nearest tenth).

The variance is .

The standard deviation is .

Step-by-step explanation:

We have the following data set:

The variance measures how far a data set is spread out. It is mathematically defined as the average of the squared differences from the mean.

To find variance we use the following formula:

Step 1: Find the mean .

The mean of a data set is the sum of the terms divided by the total number of terms.

Step 2: Create the below table.

Step 3: Find the sum of numbers in the last column.

Step 4: Calculate variance using the above formula.

The standard deviation measures how close the set of data is to the mean value of the data set.

To find standard deviation we use the following formula

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°