Standard Deviation and Square Footage Essay

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Words: 1087
Pages: 5

Chapter 2 Instructions
Practice Problem 11, 12, 13, 16, & 21
Due Week 3 Day 7 (Monday)

Follow the instructions below to submit your answers for Chapter 2 Practice Problem 11, 12, 13 16, & 21.

1. Save Chapter 2 Instructions to your computer.
2. Type your answers beside the appropriate symbol below.
3. Resave this form.
4. Attach the resaved form to your reply when you turn-in your work in the Assignments section of the Classroom tab. Note: Each question will be listed separately in the assignments section; however, you only need to submit this form one time to turn-in your answers.

Below is an explanation of the symbols in Chapter 2.

M = Mean
Mdn. = Median
SS = Sum of Squared Deviations
SD2 = Variance
SD = Standard Deviation

Read each question in your text book and then type your answers for Chapter 2 Practice Problem 11, 12, 13, & 16 in the corresponding spaces below. Round your answers to 2 decimal places.

11. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:
2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 1, 4, 3, 4, 2, 1, 0

M = =2.00 As the number of observations, n, is odd, so the median is the value of the middle term of sorted observations.
Here n=21, so median is the value of 11th observation. Mdn. = 2.00

SS = =56.00 SD2 = = 2.80 SD = = 1.67

12. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation: 1,112; 1,245; 1,361; 1,372; 1,472 M = =1,312.40 Mdn. = Median is the 3rd sorted observation=1,361.00 SS = =76,089.20 SD2 = =19,022.30 SD = =137.92

13. 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

M = =3.17 Mdn. = Average of 3rd and 4th sorted observations
= (3.2+3.3)/2=3.25 SS == 0.53 SD2 = =0.11 SD = =0.33

16. A psychologist interested in political behavior measured the square footage of the desks in the official office of four U.S. governors and of four chief executive officers (CEOs) of major U.S. corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the CEOs were 32, 60, 48, and 36 square feet. (a) Figure the means and standard deviations for the governors and for the CEOs. (b) Explain, to a person who has never had a course in statistics, what you have done. (c) Note the ways in which the means and standard deviations differ,and speculate on the possible meaning of these differences, presuming that they are representative of U.S. governors and large corporations’ CEOs in general.

16a. Governors - M = 43.00 SD = 6.83 CEO’s - M = 44.00 SD = 12.65

16b. Explain your answer below:

Mean is the average of all the sample values. So, here on an average 43 square footage is the area of the desks of the official office of US governors. Whereas 44 square footage is the average office area of CEOs of major US corporations. As expected not all the governor’s or CEO’s office has the same value of 43 or 44 square footage. Some will be more or some will be less. There is some variation in the area. This variation is 6.83 square footage for US governors; whereas 12.65 square footage for CEO’s office.

16c. Explain below how the means and standard deviations differ:

Here, we see that mean of CEO’s office area is slightly more than that of governor’s office area; 44 compared to 43. But when we see the variability, it is clear that governor’s space is much more consistent whose standard deviation is 6.83. In case of CEO’s office space this variability is almost double of governor’s space. It means that some of the CEO enjoys more office space whereas some of them enjoys very less. But, in case of governor’s office space, it is very much consistent; they are having almost similar amount of office…