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

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%

...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, where you add up all the numbers and then divide by the...

...as the arithmetic mean or simply the mean. The mean is a measure of the center of the data. Average and mean are used interchangeably to label the result of the sum of all measurements divided by the number of measurements. In mathematical notation the formula for calculating the sample mean is given below.
If the value given represents the mean of all values in a population it is...

...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 intervals – the range of
values – being used.
It is from these classes, are upper and
lower class boundaries found.
Mean...

...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 intervals – the range of
values – being used.
It is from these classes, are upper and
lower class boundaries found.
Mean...

...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, where you add up all the numbers and then divide by the...

...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 all the data in a set divided by the number of values in that set....

...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 of variation used in the study? Amongst the data collected several variations were introduced. These...

...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
making your text bold.
There are a number of ways to alter the size of your text in HTML, I
am going to show you what I feel is the easiest, you can use
numbers ranging from 1 - 7 (1 is small, 7 is large)
THIS IS SIZE 1
THIS IS SIZE 2
THIS IS SIZE 3
THIS IS SIZE 4
THIS IS SIZE 5
THIS IS SIZE 6...

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