For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation
3.0, 3.4, 2.6, 3.3, 3.5, 3.2
What don't you understand about this assignment?
You want to estimate the mean of a population within + 3 with 90 % confidence If the population
standard deviation is = 8, how large of a sample is needed?
1558
To find the mean, median, sum of squared deviations, variance, and standard deviation for the given scores, follow these steps:
1. Mean (a):
- Add up all the numbers: 3.0 + 3.4 + 2.6 + 3.3 + 3.5 + 3.2 = 19.0
- Divide the sum by the total number of scores: 19.0 / 6 = 3.1667 (rounded to four decimal places)
- The mean is 3.1667.
2. Median (b):
- Arrange the scores in ascending order: 2.6, 3.0, 3.2, 3.3, 3.4, 3.5
- As there are six scores, the median is the average of the two middle values.
- The middle values are 3.2 and 3.3, so the median is (3.2 + 3.3) / 2 = 3.25
- The median is 3.25.
3. Sum of squared deviations (c):
- To calculate the sum of squared deviations, we need to find the deviation of each score from the mean, square them, and then add them up.
- Deviation from mean = score - mean
- For each score:
- (3.0 - 3.1667)^2 = 0.02778
- (3.4 - 3.1667)^2 = 0.05278
- (2.6 - 3.1667)^2 = 0.32444
- (3.3 - 3.1667)^2 = 0.01778
- (3.5 - 3.1667)^2 = 0.11111
- (3.2 - 3.1667)^2 = 0.00042
- Sum of squared deviations = 0.02778 + 0.05278 + 0.32444 + 0.01778 + 0.11111 + 0.00042 = 0.53431
- The sum of squared deviations is 0.53431.
4. Variance (d):
- Variance is the average of the squared deviations from the mean.
- Variance = sum of squared deviations / total number of scores
- Variance = 0.53431 / 6 = 0.08905 (rounded to five decimal places)
- The variance is 0.08905.
5. Standard deviation (e):
- The standard deviation is the square root of the variance.
- Standard deviation = √(variance)
- Standard deviation = √(0.08905) = 0.2984 (rounded to four decimal places)
- The standard deviation is approximately 0.2984.