Mgt 512 - Homework Solutions - Chapters 2 and 3

MGT512. Homework Solutions. Chapters 2 and 3.

Problem 1. Compute the (a) mean, (b) MAD, (c) variance, and (d) standard deviation using the sample data below. I recommend that you try doing this by hand to understand how to apply the formulas (but feel free to use Excel to verify your result).

{ 2,   -9,   6,   15 }

(a) Sample mean

[pic 1]

(b) MAD

[pic 2]

(c) Sample variance

[pic 3]

(d) Sample standard deviation

[pic 4]

Problem 2. Using the sample dataset below and the percentile calculation method covered in the textbook and handouts (do NOT use Excel), find the following. To show work in (a, b, d, e,): (1) write down the percentile you are trying to find, (2) write down the i (index) that you calculated, (3) write down the final answer.

Note: n = 20 (we have 20 observations in the dataset),[pic 5]

[pic 6][pic 7]

1. The first quartile (Q1). Note: the first quartile (Q1) is the 25th percentile.

Index:          i = 20*25/100=5          →        First quartile = Q1 = (16.3+16.5)/2=16.4

1. The third quartile (Q3). Note: the third quartile (Q3) is the 75th percentile[pic 8]

[pic 9][pic 10]

[pic 11]

[pic 12]

1. The IQR (interquartile range).

IQR (interquartile range) = Q3 – Q1 =22.6 – 16.4 = 6.2

1. The 77th percentile.

Index:        i = 20*77/100=15.4         →        77th percentile= X16 = 23.2

1. The 12th percentile.

Index:         i = 20*12/100=2.4        →        12th percentile= X3 = 15.4

1. The range.

Range = 29.7 – 11.7 = 18

Problem 3. Use the dataset below to answer the questions.

[pic 13]

1. What is the median?

Median is the 50th percentile, so p = 50. The sample size is 35, so n = 35