We use cookies to give you the best experience possible. By continuing we’ll assume you’re on board with our cookie policy

Mean, Median, Five Number Summary Essay Sample

essay
The whole doc is available only for registered users OPEN DOC
  • Pages:
  • Word count: 435
  • Category: data

A limited time offer!

Get a custom sample essay written according to your requirements urgent 3h delivery guaranteed

Order Now

Mean, Median, Five Number Summary Essay Sample

1. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. a) Compute the mean, median, and mode.
b) Compute the 20th, 65th, and 75th percentiles.
c) Compute the range, interquartile range, variance, and standard deviation.

Answers:
Data values: 15, 20, 25, 25, 27, 28, 30, 34
a) Mean: [pic]= ∑xi/n = (15+20+25+25+27+28+30+34) / 8 = 204 / 8 = 25.5 Median: Even number, so median is = (25+27)/2 = 26
Mode: Most frequent number = 25

b) 20th Percentile = (P/100)n = (20/100)8 = 0.2×8 = 1.6 = 2 65th Percentile = (65/100)8 = 0.65×8 = 5.2 = 6
75th Percentile = (75/100)8 = 0.75×8 = 6

c) Range: Largest data value – smallest data value = 34-15 = 19 Interquartile range: 3rd Quartile – 1st Quartile = 6 –((25/100)8) = 6-2 = 4 Variance: [pic]= (204-25.5)/8-1 = 25.5
Standard Deviation: [pic]= [pic]= 5.05

2. Consider a sample with a mean of 500 and a standard deviation of 100. What are the z-scores for the following data values: 650, 500, and 280?

Answers:
a) Data value 650: z-scores = [pic] = (650-500)/100 = 1.5 b) Data value 500: (500-500)/100 = 0
c) Data value 280: (280-500)/100 = -2.2

3. Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev’s theorem to determine the percentage of the data within each of the following ranges. a) 20 to 40
b) 15 to 45
c) 18 to 42

Answers:
Standard deviation (s) = 5
Mean ([pic]) = 30
a) z1 = (20-30)/5 = -2
z2 = (40-30)/5 = 2
(1-1/z²) = (1-1/2²) = 0.75 = 75%

b) z1 = (15-30)/5 = -3
z2 = (45-30)/5 = 3
(1-1/3²) = 0.89 = 89%

c) z1 = (18-30)/5 = -2.4
z2 = (42-30)/5 = 2.4
(1-1/2.4²) = 0.83 = 83%

4. Suppose the data have a bell-shaped distribution with a mean of 30 and a standard deviation of 5. Use the empirical rule to determine the percentage of data within each of the following ranges. a) 20 to 40

b) 15 to 45
c) 25 to 35

Answers:
Standard deviation (s) = 5
Mean ([pic]) = 30
a) z1 = (20-30)/5 = -2
z2 = (40-30)/5 = 2
By empirical rule, there are at approximately 95% of the data values will be within this interval.

b) z1 = (15-30)/5 = -3
z2 = (45-30)/5 = 3
By empirical rule, there are at approximately 99.7% of the data values will be within this interval.

c) z1 = (25-30)/5 = -1
z2 = (35-30)/5 = 1
By empirical rule, there are at approximately 68% of the data values will be within this interval.

We can write a custom essay

According to Your Specific Requirements

Order an essay
Get Access To The Full Essay
icon
300+
Materials Daily
icon
100,000+ Subjects
2000+ Topics
icon
Free Plagiarism
Checker
icon
All Materials
are Cataloged Well

Sorry, but copying text is forbidden on this website. If you need this or any other sample, we can send it to you via email.

By clicking "SEND", you agree to our terms of service and privacy policy. We'll occasionally send you account related and promo emails.
Sorry, but only registered users have full access

How about getting this access
immediately?

Become a member

Your Answer Is Very Helpful For Us
Thank You A Lot!

logo

Emma Taylor

online

Hi there!
Would you like to get such a paper?
How about getting a customized one?

Can't find What you were Looking for?

Get access to our huge, continuously updated knowledge base

The next update will be in:
14 : 59 : 59
Become a Member