Examples & Exercises of Discrete Data & Continuous Data
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Friday, June 10, 2016
Statistical Data
Introduction
Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or social problem, it is convenient to begin with a statistical population or a statistical model process to be studied
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Measure of Central Tendency Part - The Mode
The mode is the most commonly occurring value in a distribution.
Consider this dataset showing the retirement age of 11 people, in whole years:
54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60
This table shows a simple frequency distribution of the retirement age data.
The most commonly occurring value is 54, therefore the mode of this distribution is 54 years.
Consider this dataset showing the retirement age of 11 people, in whole years:
54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60
This table shows a simple frequency distribution of the retirement age data.
Age
|
Frequency
|
54
|
3
|
55
|
1
|
56
|
1
|
57
|
2
|
58
|
2
|
60
|
2
|
The most commonly occurring value is 54, therefore the mode of this distribution is 54 years.
Measures of Central Tendency - The Median
The median is the middle value in distribution when the values are arranged in ascending or descending order.
The median divides the distribution in half (there are 50% of observations on either side of the median value). In a distribution with an odd number of observations, the median value is the middle value.
Looking at the retirement age distribution (which has 11 observations), the median is the middle value, which is 57 years:
54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60
When the distribution has an even number of observations, the median value is the mean of the two middle values. In the following distribution, the two middle values are 56 and 57, therefore the median equals 56.5 years:
52, 54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60
The median divides the distribution in half (there are 50% of observations on either side of the median value). In a distribution with an odd number of observations, the median value is the middle value.
Looking at the retirement age distribution (which has 11 observations), the median is the middle value, which is 57 years:
54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60
When the distribution has an even number of observations, the median value is the mean of the two middle values. In the following distribution, the two middle values are 56 and 57, therefore the median equals 56.5 years:
52, 54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60
Measure of Central Tendency - The Mean
The mean is the sum of the value of each observation in a dataset divided by the number of observations. This is also known as the arithmetic average.
Looking at the retirement age distribution again:
54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60
The mean is calculated by adding together all the values (54+54+54+55+56+57+57+58+58+60+60 = 623) and dividing by the number of observations (11) which equals 56.6 years.
Looking at the retirement age distribution again:
54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60
The mean is calculated by adding together all the values (54+54+54+55+56+57+57+58+58+60+60 = 623) and dividing by the number of observations (11) which equals 56.6 years.
Introduction to Measures of Central Tendency
Measures of Central Tendency
Introduction
A measure of central tendency is a value that attempts to describe a set of data by identifying the center position in the data set. Therefore, measures of central tendency sometimes called measures of central location. They are also classified as summary statistics. The mean (often called the average) is most likely the measure of central tendency that you are most familiar with, but there are others, such as the median and the mode.
The mean, median and mode are all valid measures of central tendency, but under different conditions, some measures of central tendency become more convenient to use than others. In the following sections, we will look at the mean, mode and median, and learn how to calculate them and under what conditions they are most appropriate to be used.
Measure of central tendency
- Mean
- Median
- Mode
Measure of Central Tendency Exercises
1.
The week salaries of six employees at McDonalds
are $140, $220, $90, $180, $140, $200. For these six salaries; find: (a) the
mean (b) the median (c) the mode.
Linear Inequalities
In mathematics of linear inequalities are inequalities involving linear functions. A linear inequality contains one of the symbols of inequality: < is less than. > is greater than. ≤ is less than or equal to.
Following is a video of linear inequalities:-
Following is a video of linear inequalities:-
Indices
The index is a useful way to easily express large amounts. They also present us with many useful features to manipulate them using the so-called Law Index.
The expression 25 is defined as follows:
25 = 2 x 2 x 2 x 2 x 2
We call "2" the base and "5" the index
Below are the video of indices:-
Logarithm
In mathematics, the logarithm is the reverse operation exponentiation. This means that the logarithm of a number is the exponent of another fixed value, the base, must be raised to produce that number. In simple cases of repeated accusations logarithmic multiplication. For example, the base 10 logarithm of 1000 is 3, as 10 to the power 3 is 1000(1000 = 10 × 10 × 10 = 103); the multiplication is repeated three times. More commonly, exponentiation allow any positive real number will be raised to any real power, always positive results, so the logarithm can be calculated for any two positive real numbers and x b where b is not equal to 1.The logarithm of x to base b, denoted logb(x), is the unique real number y such that
- by = x.
For example, as 64 = 26, then:
- log2(64) = 6
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