top-rated free essay

Mean, Median, Five Number Summary

By Indofood1 Jan 09, 2013 477 Words
Name:E.
Student ID:2011
Country:
Course:Business Statistics
Homework 2

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 = 0.2x8 = 1.6 = 2 65th Percentile = (65/100)8 = 0.65x8 = 5.2 = 6
75th Percentile = (75/100)8 = 0.75x8 = 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.

Cite This Document

Related Documents

  • Mean, Median, Mode

    ...Mean, Median, Mode, and Range Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all. The "mean" is the "average" you're used to, wh...

    Read More
  • Mean Mode and Median

    ...Mean, Mode and Median Ungrouped and Grouped Data Ungrouped Data refers to raw data that has been ‘processed’; so as to determine frequencies. The data, along with the frequencies, are presented individually. Grouped Data refers to values that have been analysed and arranged into groups called ‘class’. The classes are based on interval...

    Read More
  • Mean Mode and Median

    ...Mean, Mode and Median Ungrouped and Grouped Data Ungrouped Data refers to raw data that has been ‘processed’; so as to determine frequencies. The data, along with the frequencies, are presented individually. Grouped Data refers to values that have been analysed and arranged into groups called ‘class’. The classes are based on interval...

    Read More
  • Mean,Median, mode and range

    ...Mean, Median, Mode, and Range Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all. The "mean" is the "average" you are used to, ...

    Read More
  • Mean and Median

    ...1.Mean and median are used as the primary measurement. Mode is seen in the first table and table 3 Appropriate measure of central tendency? Absolutely, the mean is clearly stated and many variations are introduced. Comparisons between years are used to show increases or decreases within the infant mortality rate. 2. How were measures...

    Read More
  • Mean, Median, Mode

    ...Mean, median, and mode are differing values that furnish information regarding a set of observations. The mean is used when one desires to determine the average value for data ranked in intervals. The median is used to learn the middle of graded information, and the mode is used to summarize non-numeric data. The mean is equal to the amount of ...

    Read More
  • being mean

    ...guides written by me! End of my meaningless paragraph of text!" TIP: The spelling "center" is American, if you use the English spelling "Centre" your HTML will not work. ©2006 Dan Thompson – All Rights Reserved - 18 - Basic HTML by El Passo Books v2.0 5. Now for the final part of the chapter! Sizing, underlining and ma...

    Read More
  • High Five Book Summary

    ...High Five! The Magic of Working Together lists and explains four keys to a successful team and reasons that when all four keys are properly used, the team becomes a high-five team. Blanchard and Bowles use the thrill of a high-five coming together to describe the thrill of a team working together, which is where the term high-five team comes fro...

    Read More

Discover the Best Free Essays on StudyMode

Conquer writer's block once and for all.

High Quality Essays

Our library contains thousands of carefully selected free research papers and essays.

Popular Topics

No matter the topic you're researching, chances are we have it covered.