What is the standard deviation of the following data set rounded to the nearest tenth? 3, 17, 18, 15, 12, 21, 9 6.0 5.8 5.7 6.1
What is the standard deviation of the following data set rounded to the nearest tenth? 3, 17, 18, 15, 12, 21, 9 6.0 5.8 5.7 6.1
I think that it is c or d but correct me if i am wrong
Hey,
To find the Standard deviation of the data set, there are 4 steps:
1. Work out the Mean (the simple average of the numbers)
2. Then for each number: subtract the Mean and square the result.
3. Then work out the mean of those squared differences.
4. Take the square root of that and we are done!
Here is your
6.1
Is there a typo? I have checked my answer multiple times. Perhaps are you missing a number in the data set?
Cheers,
Izzy
The standard deviation of the data set is 5.7 to the nearest tenth
Step-by-step explanation:
* Lets explain how to find the standard deviation
# Step 1: find the mean of the data set
∵ The mean = the sum of the data ÷ the number of the data
∵ The data set is 3 , 17 , 18 , 15 , 12 , 21 , 9
∵ Their sum = 3 + 17 + 18 + 15 + 12 + 21 + 9 = 95
∵ They are seven
∴ The mean = 95 ÷ 7 = 13.6
# Step 2: subtract the mean from each data and square the answer
∴ (3 - 13.6)² = 112.36
∴ (17 - 13.6)² = 11.56
∴ (18 - 13.6)² = 19.36
∴ (15 - 13.6)² = 1.96
∴ (12 - 13.6)² = 2.56
∴ (21 - 13.6)² = 54.76
∴ (9 - 13.6)² = 21.16
# Step 3: find the mean of these squared difference
∵ The mean = the sum of the data ÷ the number of the data
∵ The sum = 112.36 + 11.56 + 19.36 + 1.96 + 2.56 + 54.76 + 21.16 = 223.72
∴ The mean = 223.72 ÷ 7 = 31.96
# Step 4: the standard deviation is the square root of this mean
∴ The standard deviation = √(31.96) = 5.6533 ≅ 5.7
* The standard deviation of the data set is 5.7 to the nearest tenth