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
Do you mean that you're in a psychology class and can't find the mean or the median???
What about the others?
To find the mean of the scores, add up all the scores and divide by the total number of scores.
(a) Mean:
3.0 + 3.4 + 2.6 + 3.3 + 3.5 + 3.2 = 19
Mean = 19 / 6 = 3.17 (rounded to two decimal places)
To find the median, arrange the scores in ascending order and find the middle value. If there is an even number of scores, find the average of the two middle values.
(b) Median:
2.6, 3.0, 3.2, 3.3, 3.4, 3.5 (arranged in ascending order)
Median = (3.2 + 3.3) / 2 = 3.25
To find the sum of squared deviations, subtract the mean from each score, square the result, and sum all the squared deviations.
(c) Sum of squared deviations:
(3.0 - 3.17)^2 + (3.4 - 3.17)^2 + (2.6 - 3.17)^2 + (3.3 - 3.17)^2 + (3.5 - 3.17)^2 + (3.2 - 3.17)^2
= 0.0289 + 0.0144 + 0.0329 + 0.0009 + 0.0100 + 0.0009
Sum of squared deviations = 0.0879
To find the variance, divide the sum of squared deviations by the total number of scores minus one.
(d) Variance:
Variance = 0.0879 / (6 - 1) = 0.0176
To find the standard deviation, take the square root of the variance.
(e) Standard deviation:
Standard deviation = √0.0176 = 0.1326 (rounded to four decimal places)