Find the range population of Ethan and the population standard deviation
Ethan: 9, 24, 8, 9, 5, 8, 9, 10, 8, 10
range is lowest to hightest: 5 to 24, although many would throw out 24 as an outlier (look that word up)
standard deviation, best done on your calculator, but http://www.calculator.net/standard-deviation-calculator.html?numberinputs=9%2C+24%2C+8%2C+9%2C+5%2C+8%2C+9%2C+10%2C+8%2C+10&x=30&y=26
and if you throw out the outlier, look at what happens to mean and std deviation.
http://www.calculator.net/standard-deviation-calculator.html?numberinputs=9%2C8%2C+9%2C+5%2C+8%2C+9%2C+10%2C+8%2C+10&x=60&y=25
To find the range of a set of numbers, you need to find the difference between the largest and smallest numbers in the set.
For the population standard deviation, you can follow these steps:
1. Find the mean (average) of the population.
2. Subtract the mean from each number in the population.
3. Square each difference obtained in step 2.
4. Find the mean of the squared differences.
5. Take the square root of the mean obtained in step 4.
Now let's calculate the range and population standard deviation for Ethan's population:
Population: 9, 24, 8, 9, 5, 8, 9, 10, 8, 10
1. To calculate the range, we find the difference between the largest and smallest numbers:
Largest number: 24
Smallest number: 5
Range = Largest number - Smallest number = 24 - 5 = 19
2. To calculate the mean, we sum up all the numbers and divide by the total count:
Mean = (9 + 24 + 8 + 9 + 5 + 8 + 9 + 10 + 8 + 10) / 10 = 100 / 10 = 10
3. Subtract the mean from each number in the population:
Subtracting 10 from each number: -1, 14, -2, -1, -5, -2, -1, 0, -2, 0
4. Square each difference:
Squaring the differences: 1, 196, 4, 1, 25, 4, 1, 0, 4, 0
5. Find the mean of the squared differences:
Mean = (1 + 196 + 4 + 1 + 25 + 4 + 1 + 0 + 4 + 0) / 10 = 236 / 10 = 23.6
6. Take the square root of the mean:
Population standard deviation = √23.6 = √(23.6) = 4.856
Therefore, the range of the population is 19 and the population standard deviation is approximately 4.856.