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. It is typically used with continuous figures. The result will probably not be one of the values in the data set, but is a representation of all those values. In other words, if I want to find the mean salary at a particular company, I would add together all the salaries and divide by the total number of salaries added: $50,000 + $56,000 + $54,500 = $53,500. The problem with mean figures is they are easily slanted by one figure that stands far above or below the others. In the previous example, if I have three annual salaries of $50,000, $56,000, and $54,500, and then the company president’s salary of $260,000, I will derive an average salary of $105,125. This mean is double the actual salaries of the lower paid workers. In this case it would be more appropriate to find the median salary. To find the median salary in the previous example, we arrange the data according to value: $50,000, $54,500, $56,000, and $260,000 and find the middle which would be $55,250. If I wanted to know the breakdown of salaries in the company, I would use mode. Using this method, I could compile data that reveals of the four persons working at the company, two earn $46,000 to $55,000; one earns $56,000 to $65,000; and one earns above $66,000. Using mode, we could also measure how many of the four employees belong to a particular gender, race, and so forth.

...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 number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.
The "range" is just the difference between the largest and smallest values.
Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13
The mean is the usual average, so:
(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15
Note that the mean isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.
The median is the middle value, so I'll have to rewrite the list in order:
13, 13, 13,...

...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.MeanMean
The
‘Mean’ is the total of all the values in the set of data divided by the
total number of values in a set of data.
The arithmetic mean (or simply "mean") of a sample is the sum the
sampled values divided by the number of items in the sample.
x is the value of a member of the set of data
f is the frequency or number of members of the set of data
Mean=
Therefore: = 6.56
Grades
Frequency (f)
Total Value (x)
1
5
5
2
2
4
3
7
21
4
4
16
5
4
20
6
1
6
7
8
56
8
3
24
9
5
45
10
4
40
11
4
44
12
5
60
TOTALS
52
341
Mean in relation to Grouped Data
Mean in relation to grouped data
emphasizes the usage of class
intervals. Rather than the data being
presented individually, they are
presented in groupings (called
class). It is from there a midpoint is
Grade
Intervals
Frequency (f)
1-3
14
4-6
9
7-9
16
10-12
13
reached...

...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.MeanMean
The
‘Mean’ is the total of all the values in the set of data divided by the
total number of values in a set of data.
The arithmetic mean (or simply "mean") of a sample is the sum the
sampled values divided by the number of items in the sample.
x is the value of a member of the set of data
f is the frequency or number of members of the set of data
Mean=
Therefore: = 6.56
Grades
Frequency (f)
Total Value (x)
1
5
5
2
2
4
3
7
21
4
4
16
5
4
20
6
1
6
7
8
56
8
3
24
9
5
45
10
4
40
11
4
44
12
5
60
TOTALS
52
341
Mean in relation to Grouped Data
Mean in relation to grouped data
emphasizes the usage of class
intervals. Rather than the data being
presented individually, they are
presented in groupings (called
class). It is from there a midpoint is
Grade
Intervals
Frequency (f)
1-3
14
4-6
9
7-9
16
10-12
13
reached...

...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 number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.
The "range" is just the difference between the largest and smallest values.
Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13
The mean is the usual average, so:
(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15
Note that the mean is not a value from the original list. This is a common result. You should not assume that your mean would be one of your original numbers.
The median is the middle value, so I will have to rewrite the list in order:
13, 13, 13, 13, 14, 14,...

...Statistics: Median, Mode and Frequency Distribution
Given a list of numbers,
The median is the “middle value” of a list. It is the smallest number such that at least half the numbers in the list are no greater than it. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, themedian is equal to the sum of the two middle (after sorting) numbers divided by two.
The mode is the most common (frequent) value. A list can have more than one mode.
Let’s have a look at an example:
In an experiment measuring the percentage shrinkage on drying, 30 plastic clay test specimens produced the following results (rounded to one decimal):
19.3 15.8 20.7 18.4 14.9 17.3 21.3 16.1 18.6 20.5
20.5 16.9 18.5 18.7 12.3 19.5 23.4 18.8 18.3 16.9
17.9 17.1 22.5 18.8 19.4 17.4 18.5 17.5 16.5 17.5
In order to determine the median and the mode, let’s sort the numbers in the list, starting with the smallest and ending with the biggest:
12.3 14.9 15.8 16.1 16.5 16.9 16.9 17.1 17.3 17.4 17.5 17.5 17.9 18.3 18.4 18.5 18.5 18.6 18.7 18.8 18.8 19.3 19.4 19.5 20.5 20.5 20.7 21.3 22.5 23.4
16.9, 17.5, 18.5, 18.8 and 20.5 appear twice in the list, while the other...

... 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 = 26Mode: 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)...

...The colonial overseas British empire was made possible by (modern) science in two ways. First, science provided the physical means of acquisition of territory and its control. Second, the development of the powerful intellectual system of modern science gave Europe a cultural and ethnic superiority which in turn provided legitimacy for the colonial rule. From 1869 till, say, 1914 the Indian upper class made conscientious efforts to cultivate pure science with a view to countering the ideological domination by the British. As a corollary, the role of science as a new means of production of wealth was largely ignored. Independent India's attitude towards science has been fashioned by its colonial experience. Thus India has sought to utilize applied science in furthering its foreign policy objectives. Under the Indian auspices, modern science was Brahminized during the colonial period, and Kshatriya-ized after independence. The artisanization of modern science that gave Europe its strength never took place in India.
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