find the range,standard deviation, and variance for the following sample date:
98,2,53,61,15,87,63,63,91,29,96,79,93,40,5,62
*please show all calculations for confirmation. thank you very much. i just want to double myself. thank you.
Mary,
If you want people to take you seriously, it would undoubtedly be a good idea to change your screen name to just Mary. The longer you have this "panic mode" thing showing up, the less seriously people will take your posts. It's a form of crying wolf.
Range = highest score - lowest score
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
I'll let you do the calculations.
There is a tool for that sort of calculation at :
http://easycalculation.com/statistics/standard-deviation.php
The range is obviously 2 to 98
The mean is 58.56
The standard deviation is 32.35
The variance is the square of that
To find the range, standard deviation, and variance for the given sample data, follow these steps:
1. Range:
The range is the difference between the highest and lowest values in the dataset. To find the range, arrange the data in ascending order and subtract the lowest value from the highest value.
Sample data: 2, 5, 15, 29, 40, 53, 61, 62, 63, 63, 79, 87, 91, 93, 96, 98
Range = 98 - 2 = 96
2. Variance:
Variance measures how spread out the data is from the mean. To calculate the variance, you need to follow several steps:
a. Find the mean of the data by summing up all the values and dividing by the total number of values (in this case, 16).
Sum = 2 + 5 + 15 + 29 + 40 + 53 + 61 + 62 + 63 + 63 + 79 + 87 + 91 + 93 + 96 + 98 = 1035
Mean = 1035 / 16 = 64.68 (rounded to two decimal places)
b. Calculate the deviation from the mean for each data point by subtracting the mean from each value.
Deviations: -62.68, -59.68, -49.68, -35.68, -24.68, -11.68, -3.68, -2.68, -1.68, -1.68, 14.32, 22.32, 26.32, 28.32, 31.32, 33.32
c. Square each deviation to eliminate negative values.
Squared deviations: 3930.5424, 3555.5424, 2469.5424, 1273.5424, 609.5424, 136.5424, 13.5424, 7.1824, 2.8224, 2.8224, 204.4224, 497.2224, 690.4224, 795.7824, 983.2224, 1107.6224
d. Find the sum of these squared deviations.
Sum of squared deviations = 14131.16 (rounded to two decimal places)
e. Divide this sum by the total number of values (16) to get the variance.
Variance = 14131.16 / 16 = 882.9475 (rounded to four decimal places)
3. Standard Deviation:
The standard deviation is the square root of the variance. To find the standard deviation, take the square root of the variance calculated in the previous step.
Standard Deviation = √(882.9475) = 29.7007 (rounded to four decimal places)
In summary, we have:
- Range: 96
- Variance: 882.9475
- Standard Deviation: 29.7007