Directions: In cooperative groups of two to three, please complete Part A: Measures of Variability Assignment.

Part A: Measures of Variability:
Although measures of central tendency provide useful information about data sets, do they adequately describe the data if used as only descriptive or summary statistics? Please consider the four sets below.

Please complete the mean and median for each data set (Data Sets' A-D), analyze the results and interpret the adequacy of summary statistics. If there is an inadequacy, what do you propose should be reported?

Data:
Set A: 100, 100, 100, 100, 100, 100
Set B: 110, 105, 100, 100, 95, 90
Set C: 155, 130, 110, 90, 65, 50
Set D: 200, 150, 125, 75, 50, 0

Cooperative GroupCecilia and Katherine
Data Set MeanA: M 100
Data Set MedianA: MDN 100
Data Set Analysesthere is no variability in distribution

B: M 100
B: MDN 100
the scores cluster around the mean

C: M 100
C: MDN 100
there is more variability in scores similar to a normal distribution

D: M 100
D: MDN 100
the data (mean and median) alone does not indicate the true variability of scores
Svetlana K and Marva R


The mean and the median for all four sets is the same, there is no true indication
of variability.
Annie L, Eileen B, Maria O
A : 100
A: 100
There is no standard deviation because all data is 100.

B: 100
B:100
The standard deviation for data set B is 5.

C:100
C:100
The standard deviation for data set C is 10.

D: 100
D:100
The standard deviation for set D is 25. As the standard deviation increases so does
the variance which makes the data weaker.
Eric & Marquita
Mean for each data set was 100.
Median for each data set was 100.
Summary statistics are inadequate for interpreting the data.

Melinda & Marion
A) 100
A) 100
The distribution of numbers are all the same and thus both the mean and median remain the same.

B) 100
B) 100
The distribution of numbers are relatively close to the mean and median.

C) 100
C) 100
The distribution of numbers are more spread out from the mean and median.

D) 100
D) 100
The distribution of numbers are greatly spread out from each other. The wide distribution give misleading information when solely looking at the mean and median.
Kettely & Clara
A: 100
B: 100
C: 100
D: 100
A: 100
B: 100
C: 100
D: 100
Data set present no standard deviation. Distribution of numbers are all the same.
The distribution of numbers are close, clustered around the mean and median.
The distribution of numbers are spread out. The set present variability in scores similar to a normal distribution.
The distribution of numbers is widely dispersed, but the mean and median remained the same compared with the other data sets.




































Part B: Mean and Standard Deviation:
As you can see, measures of central tendency do not convey information about how similar (homogeneity) or dissimilar (heterogeneity) the data sets can be. This varying of data, or dispersion of scores, is referred to as "measures of variability/measures of dispersion or scatter." The measures of variability which we will consider in this practice problem are range, standard deviation, and variance.
The range describes the spread of numerical values for interval and rational data. It has limited capability.
The standard deviation (SD) and variance provide more useful information about relative homogeneity or hetergeneity of interval and ratio data sets. Both of these measures indicate the extent to which the data set deviate from or vary from the mean. Since the variance is simply the square of the standard deviation (or the standard deviation of the square root of the variance), either of these measures are reported in research literature. However the mean is always reported with one of the above measures and togther they provide a pair of summary statistics.
Directions: In cooperative groups, please complete the mean and standard deviation (to nearest tenth) for the following set of upgrouped data: 8, 11, 12, 13, 13, 16, 17, 18, 18
Step 1: Determine the Mean (average of all scores)
Step 2: Determine the value of the sum of x squared ( please remember x refers to your data)
For example: data set 3, 2, 4: x squared = 81 because 3 + 2 + 4 = 9 and 9 squared =81.
Step 3: Evaluate the formula for Standard Deviation (SD):
SD = the square root of the sum of x squared divided by the total number of scores (N) - in this case, N = 9 .


For your ARP, you should compute the mean and standard deviation for your dependent variable, analyze the dispersion of scores, and compare your findings with the normal curve.( see handout).

Cooperative GroupAnnie L, Eileen B, Maria O
Step 1 MeanMean= 14
Step 2Value of Sum of x squared96
Evaluate the formulas for SD and varianceThe standard deviation for this set of numbers is 3.3 and the variance is 10.7
Katherine V. and Cecilia G.
Mean= 14
96
The SD is 3.3 and the variance is 10.7...the scores cluster close to the mean, the scores are relatively homogeneous
Svetllana and Marva
Mean =14
96
The standard deviation is 3.3 and the variance is 10.7. The scores are clustered around the mean.
Eric & Marquita
Mean = 14
Value of Sum of x squared = 96
Standard deviation = 3.3; Variance = 10.7
Melinda & Marion
Mean = 14
96
The standard deviation is 3.3 with a variance of 10.7. These scores are relatively close to the mean these scores are homogenous since data sets are similar.
Kettely & Clara
Mean=14
Value of Sum of x squared=96
The standard deviation is 3.3 (√ 10.9= 3.3) and varience is 10.7 (96÷9=10.7). The scores are close to the mean, as a result we have homogeneous set.