# Find the range and standard deviation of the set of data.?

Find the range and standard deviation of the set of data.

160, 165, 170, 175, 180, 185, 190

The range is______

The standard deviation is_______

### 1 Answer

- PuzzlingLv 74 months ago
The method is exactly the same as your other question.

What's the biggest number? 190

What's the smallest number? 160

What's the difference? 190 - 160 = 30

That's the *range*.

What's the mean (average) of the 7 numbers:

(160 + 165 + 170 + 175 + 180 + 185 + 190) / 7

= 175

Note: Because the numbers go up in a progression of 5 each time, the average will be the same as the middle number. A quick tip if you need to figure this out quickly.

Now square the difference between each number and this mean:

160 - 175 = -15 --> (-15)² = 225

165 - 175 = -10 --> (-10)² = 100

170 - 175 = -5 --> (-5)² = 25

etc.

Assuming this is the complete *population* of data, we add those up and divide by *7*. (I don't see any mention that this is a *sample* of data).

(225 + 100 + 25 + 0 + 25 + 100 + 225) / 7

= 100

Remember, that's the *variance*. To get the standard deviation, take the square root.

s.d. = √100

s.d. = 10