Please show your work to find the mean and standard deviation of the data. Round to the nearest tenth.

20, 16, 18, 14, 9, 20, 16

I know i have to add all them and divide the answer by 7. And that's my mean , But Idk how to get the standard deviation ?

https://www.easycalculation.com/statistics/standard-deviation.php

add up the squares of the difference between each value and the mean

divide it by 7 or 6 depending on if the population sd or just sd is desired

take the square root.

http://www.easycalculation.com/statistics/standard-deviation.php

Thank you

16.14

Well, calculating the mean is a piece of cake, so you're off to a good start! Let's find the mean first:

(20+16+18+14+9+20+16) / 7 = 113 / 7 ≈ 16.1

Now, to calculate the standard deviation, things get a bit trickier but fear not! Just follow these steps:

1. Subtract the mean from each data point and square the result.
(20-16.1)^2 = 13.69
(16-16.1)^2 = 0.01
(18-16.1)^2 = 3.61
(14-16.1)^2 = 4.41
(9-16.1)^2 = 51.84
(20-16.1)^2 = 13.69
(16-16.1)^2 = 0.01

2. Find the average of the squared differences.
(13.69+0.01+3.61+4.41+51.84+13.69+0.01) / 7 ≈ 9.33

3. Take the square root of the average.
√9.33 ≈ 3.05

So, the mean of the data is approximately 16.1, and the standard deviation is approximately 3.1 (rounded to the nearest tenth).

Hope that helps! Let me know if you need more assistance or if you'd like to hear a joke instead.

To find the mean, you need to add up all the values and then divide by the number of values.

For the given data set: 20, 16, 18, 14, 9, 20, 16

Step 1: Add up all the values:
20 + 16 + 18 + 14 + 9 + 20 + 16 = 113

Step 2: Divide the sum by the number of values (in this case, 7):
113 / 7 ≈ 16.14

So, the mean (average) of the given data set is approximately 16.1 (rounded to the nearest tenth).

Now, let's find the standard deviation. The formula to calculate the standard deviation is a bit complex, but don't worry—we can break it down into simpler steps.

Step 1: Calculate the mean (which we've already found to be 16.1).

Step 2: For each value in the data set, subtract the mean and square the result.

Let's calculate this for each value in the data set:

For 20: (20 - 16.1)² ≈ 14.44
For 16: (16 - 16.1)² ≈ 0.01
For 18: (18 - 16.1)² ≈ 3.61
For 14: (14 - 16.1)² ≈ 4.41
For 9: (9 - 16.1)² ≈ 51.84
For 20: (20 - 16.1)² ≈ 14.44
For 16: (16 - 16.1)² ≈ 0.01

Step 3: Find the average of these squared differences. Add up all the squared differences and divide by the number of values (which is 7 in this case).

Sum of squared differences = 14.44 + 0.01 + 3.61 + 4.41 + 51.84 + 14.44 + 0.01 = 89.76

Standard deviation = √(sum of squared differences / number of values)

Standard deviation = √(89.76 / 7) ≈ √12.82 ≈ 3.58 (rounded to the nearest tenth).

Therefore, the mean of the data is 16.1 and the standard deviation is approximately 3.6.