# The data lists the average monthly snowfall for Jan. in 15 cities in the US 20 13 15 28 16 25 2 14 35 42 5 34 34 38 29find the mean , variance and standard deviation please show all work

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To find the **mean**, add the numbers and divide by 15 because there are 15 numbers in the data set.

20 + 13 + 15 + 28 + 16 + 25 + 2 + 14 + 35 + 42 + 5 + 34 + 34 + 38 + 29 = 350

350 / 15 = 23.3333...

To find the **variance**, subtract each number from the mean, square the difference, and then find the mean of the squared differences.

(20 - 23.3333)^2 = 11.1111

(13 - 23.3333)^2 = 106.7777

(15 - 23.3333)^2 = 69.4444

(28 - 23.3333)^2 = 21.7777

(16 - 23.3333)^2 = 53.7777

(25 - 23.3333)^2 = 2.7777

(2 - 23.3333)^2 = 455.1111

(14 - 23.3333)^2 = 87.1111

(35 - 23.3333)^2 = 136.1111

(42 - 23.3333)^2 = 348.4444

(5 - 23.3333)^2 = 336.1111

(34 - 23.3333)^2 = 113.7777

(34 - 23.3333)^2 = 113.7777

(38 - 23.3333)^2 = 215.1111

(29 - 23.3333)^2 = 32.1111

11.1111 + 106.7777 + 69.4444 + 21.7777 + 53.7777 + 2.7777 + 455.1111 + 87.1111 + 136.1111 + 348.4444 + 336.1111 + 113.7777 + 113.7777 + 215.1111 + 32.1111 = 2103.3327

2103.3327 / 15 = 140.22218

To find the **standard deviation**, take the square root of the variance.

`sqrt(140.22218)` `~~` 11.84

To summarize:

**mean `~~` 23.3**

**variance `~~` 140.2**

**standard deviation `~~` 11.8**