Find the standard deviation for the data. Round your answer to one more decimal place than the original data.
{15,13,31,42,58,78}
To find the standard deviation for a set of data, you can follow these steps:
1. Find the mean (average) of the data set. Add up all the numbers and divide the sum by the total number of data points.
Mean = (15 + 13 + 31 + 42 + 58 + 78) / 6 = 237 / 6 = 39.5
2. Subtract the mean from each data point and square the result for each data point.
(15 - 39.5)^2 = 616.25
(13 - 39.5)^2 = 676.25
(31 - 39.5)^2 = 71.25
(42 - 39.5)^2 = 6.25
(58 - 39.5)^2 = 343.75
(78 - 39.5)^2 = 1518.25
3. Find the average of these squared differences by adding them up and dividing by the total number of data points.
Average of squared differences = (616.25 + 676.25 + 71.25 + 6.25 + 343.75 + 1518.25) / 6 = 3232 / 6 = 538.67
4. Take the square root of the average of squared differences to find the standard deviation.
Standard deviation = √(538.67) ≈ 23.2
Rounded to one more decimal place than the original data, the standard deviation is 23.2.
To find the standard deviation for the given data set {15, 13, 31, 42, 58, 78}, follow these steps:
Step 1: Find the mean (average) of the data set.
Mean = (15 + 13 + 31 + 42 + 58 + 78) / 6 = 237 / 6 = 39.5
Step 2: Find the deviation of each value from the mean.
Deviation from the mean = (15 - 39.5), (13 - 39.5), (31 - 39.5), (42 - 39.5), (58 - 39.5), (78 - 39.5)
= -24.5, -26.5, -8.5, 2.5, 18.5, 38.5
Step 3: Square each deviation.
Square of deviation = (-24.5)^2, (-26.5)^2, (-8.5)^2, (2.5)^2, (18.5)^2, (38.5)^2
= 600.25, 702.25, 72.25, 6.25, 342.25, 1482.25
Step 4: Find the sum of the squared deviations.
Sum of squared deviations = 600.25 + 702.25 + 72.25 + 6.25 + 342.25 + 1482.25
= 3205.5
Step 5: Divide the sum of squared deviations by the number of values (n).
Variance = sum of squared deviations / n = 3205.5 / 6 = 534.25
Step 6: Find the square root of the variance to get the standard deviation.
Standard deviation = √variance = √534.25 ≈ 23.11
Therefore, the standard deviation for the given data set is approximately 23.1 (rounded to one more decimal place than the original data).
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.