# What are the differences in the means and variances?

Descriiptives Homework

Save this on your computer as a Word document. Answer the questions, save your work and then email your work to me as an attachment, send via Canvas, or scan your work in as a pdf attachment. If you do write your work out and scan it in, be sure that your work is legible, right-side up and in order! Be sure to show your work. If I just have an answer but do not see any calculations, I can’t tell how you came to your outcome and I can’t provide feedback and support in case your outcome is wrong. Since the assignment is in Word format, you have the option to add extra space if you need it to include your calculations.

When computing standard deviation, each question will alert you as to whether you should use the sample computational standard deviation formula or the population computational standard deviation formula. Review your notes on the differences between the sample and population standard deviation. To help with the organization of your data and formula, I have provided for you tables for you to place your X value and X2, which you will need to calculate the formula. It is not necessary to organize your data on the table from lowest to highest, but you can do this to help in your data organization and evaluation.

To help provide you with the standard deviation key, I have listed below the formulas for both sample and population standard deviation computational formula:

Population standard deviation formula:

σ = ΣX2 – (ΣX)2

_ __N__

N

Sample standard deviation formula:

s = Σx2 – (Σx)2

n __

n – 1

SHOW THE WORK FOR ALL QUESTIONS REQUIRING MATH and FORMULAS!!

1. The Newport Health Clinic experiments with two different configurations for serving patients. In one configuration, all patients enter a single waiting line that feeds three different physicians. In another configuration, patients wait in individual lines at three different physician stations. Waiting times (in minutes) are recorded for ten patients from each configuration.

Single line: 65, 66, 67, 68, 71, 73, 74, 77, 77, 77

a. What is the “n” value for this data set?

b. What is the mean for this data set?

c. What is the median for this data set?

d. What is the mode for this data set?

e. What is the standard deviation for this data set? For this example, you will use the sample data computational formula.

X X2

∑X =

(∑X)2 = ∑X2 =

Show your SD formula work below:

Multiple lines: 42, 54, 58, 62, 67, 77, 77, 85, 93, 100

f. What is the “n” value for this data set?

g. What is the mean for this data set?

h. What is the median for this data set?

i. What is the mode for this data set?

j. What is the standard deviation for this data set (Remember to use the sample computational formula.)

X X2

∑X =

(∑X)2 = ∑X2 =

Show your SD formula work below:

2. Based on the data that you have just calculated, which wait time is the most efficient with the least wait time between the single line vs. multiple lines?

3. After a week of practicing with the visualization technique, 20 basketball players again shot 25 free throws, and the sports psychologist recorded the number of successful shots (Remember your frequency distribution tables assignment from last week? As you see below, this data is organized in a frequency distribution table. As you recall, large amounts of data are often organized in frequency distribution tables to communicate and share data in a more organized, condense manner. Next to each score is the f or frequency of that score (how many times that score occurs in the data set). Before you begin calculating central tendency and variability, you must make a list of all your raw score values (not just the list of scores under the ‘X’ column). For example, if a value has a corresponding frequency of ‘0’, then that means that particular value is not a part of your data. If a value has a corresponding frequency of ‘3’ (for example, X=20) then you would list that value three times under the X column (20, 20, 20):

X f X f

25 1 18 0

24 1 17 0

23 1 16 1

22 4 15 0

21 4 14 1

20 3 13 0

19 3 12 1

a. What is the “N” value for this data set?

b. What is the mean for this data set?

c. What is the mode for this data set?

d. What is the median for this data set?

e. Calculate the standard deviation for this data set using the POPULATION computational formula.

X X2

∑X =

(∑X)2 = ∑X2 =

Show your SD formula work below:

4. Is it possible to have more than one mode?

5. A study was conducted to see if Physical Therapy is or is not effective. Below are progression scores compiled for both the Physical Therapy group and the Control group (those who did not receive Physical Therapy). The higher the scores, the more progress is made by the study individuals. Negative scores indicate a decline in progression. What are the differences in the means and variances? Based upon the descriiptive data, do you feel that the Physical Therapy group fared better than the Control group? Do you have any other observations about the data? (since this is a sample set, you will want to use the sample computational standard deviation formula). I placed the values in a table below for easy organization. Since there are negative values, be careful with your math!!! Remember that when squaring two negative values (i.e., multiplying them by themselves), the negatives cancel each other out and you end up with a positive. This means that you should have no negative values under your X2 column.

Physical therapy group scores X2 Control

Group scores X2

7 9

11 3

0 13

13 1

-5 4

25 3

-10 18

34 -22

7 0

18 -9

∑X =

(∑X)2 = ∑X2 = ∑X =

(∑X)2 = ∑X2 =

Calculate the mean, median, mode and SD to evaluate the differences between the two groups.

What are the differences in the means and variances?

Based upon the descriiptive data, do you feel that the Physical Therapy group fared better than the Control group?

Do you have any other observations about the data?