{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

04 Describing Data Graphically and Numerically Part 3

Example the mean number of days required to fill

Info icon This preview shows pages 25–36. Sign up to view the full content.

View Full Document Right Arrow Icon
Example: The mean number of days required to fill orders is 10.3 days for both of the suppliers. Which supplier would you prefer?
Image of page 25

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Range 26 Simplest measure of variation Difference between the largest and the smallest observations: Range = Largest value – Smallest value Example: For our previous example data set: 3310 3355 3450 3480 3480 3490 3520 3540 3550 3650 3730 3925 The range is 3925 – 3310 = 615
Image of page 26
Disadvantages of Range 27 Ignores the way in which data are distributed: 3310 3355 3450 3480 3480 3490 3520 3540 3550 3650 3730 3925 Range = 3925 – 3310 = 615 3310 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3925 Range = 3925 – 3310 = 615 Sensitive to outliers: 3310 3355 3450 3480 3480 3490 3520 3540 3550 3650 3730 3925 Range = 3925 – 3310 = 615 3310 3355 3450 3480 3480 3490 3520 3540 3550 3650 3730 10000
Image of page 27

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Interquartile Range 28 A measure of variability that overcomes the dependency on extreme values is the interquartile range (IQR ) IQR is the difference between the third quartile, Q 3 , and the first quartile, Q 1 IQR = Q 3 Q 1 IQR is is the range for the middle 50% of the data. Example: For our previous example data set: 3310 3355 3450 3480 3480 3490 3520 3540 3550 3650 3730 3925 The IQR is 3600 – 3465 = 135 Q 1 =3465 Q 3 =3600
Image of page 28
Variance 29 The variance is a measure of variability that utilizes all the data. The variance is based on the difference between the value of each observation (x i ) and the mean (this difference is also called deviation about the mean ) Population variance: Sample variance: N μ) (x σ N 1 i 2 i 2 = - = 1 - n ) x (x s n 1 i 2 i 2 = - =
Image of page 29

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Standard Deviation 30 The standard deviation is defined to be the positive square root of the variance. Most commonly used measure of variation Has the same units as the original data Population standard deviation: Sample standard deviation: N μ) (x σ N 1 i 2 i = - = 1 - n ) x (x s n 1 i 2 i = - =
Image of page 30
Example 31 Sample data: 10 12 14 15 17 18 18 24 n = 8 Mean = x = 16 4.3095 7 130 1 8 16) (24 16) (14 16) (12 16) (10 1 n ) x (24 ) x (14 ) x (12 ) x (10 s 2 2 2 2 2 2 2 2 = = - - + + - + - + - = - - + + - + - + - =
Image of page 31

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Comparing Standard Deviations 32 Same mean, but different standard deviations: Mean = 15.5 s = 3.338 11 12 13 14 15 16 17 18 19 20 21 11 12 13 14 15 16 17 18 19 20 21 Data B Data A Mean = 15.5 s = .9258 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = 4.57 Data C
Image of page 32
Coefficient of Variation 33 Measures relative variation Shows variation relative to mean Usually in percentage (%) Is useful to compare the variability of two or more sets of data measured in different units two or more sets of data that have different standard deviations and different means. C.V. for population: C.V. for sample: 100% x s CV = 100% μ σ CV =
Image of page 33

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Comparing Coefficients of Variation 34 Stock A: Average price last year = $50 Standard deviation = $5 Stock B: Average price last year = $100 Standard deviation = $5 5% 100% * $100 $5 100% * x s CV B = = = 10% 100% * $50 $5 100% * x s CV A = = = Both stocks have the same standard deviation, but stock B is less variable relative to its price
Image of page 34
The Empirical Rule 35 If the data distribution is bell-shaped, then the interval contains about 68% of the values in the population or the sample.
Image of page 35

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 36
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern