formula of finding mean in statics for all three methods .....please no spams ❌
Answers
Answer:
Median and Mode are the three measures of central tendency. Mean is the arithmetic average of a data set. This is found by adding the numbers in a data set and dividing by the number of observations in the data set. The median is the middle number in a data set when the numbers are listed in either ascending or descending order. The mode is the value that occurs the most often in a data set and the range is the difference between the highest and lowest values in a data set.
The Mean
x¯¯¯=∑xN
Here,
∑ represents the summation
X represents observations
N represents the number of observations .
The Median
If the total number of observations (n) is an odd number, then the formula is given below:
Median=(n+12)thobservation
If the total number of the observations (n) is an even number, then the formula is given below:
Median=(n2)thobservation+(n2+1)thobservation2
The Mode
Themodeisthemostfrequentlyoccuringobservationorvalue.
Solved Examples
Question: Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13
Solution:
Given data: 13, 18, 13, 14, 13, 16, 14, 21, 13
The mean is the usual average.
Mean = 13+18+13+14+13+16+14+21+139=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 will be one of your original numbers.)
The median is the middle value, so to rewrite the list in ascending order as given below:
13, 13, 13, 13, 14, 14, 16, 18, 21
There are nine numbers in the list, so the middle one will be
9+12=102=5
= 5th number
Hence, the median is 14.
The mode is the number that is repeated more often than any other, so 13 is the mode.
The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.
Mean = 15
Median = 14
Mode = 13
Range = 8
Answer:
Step-by-step explanation:
In statistics, the assumed mean method is used for calculating mean or arithmetic mean of a grouped data. If the given data is large, then this method is recommended rather than a direct method for calculating mean. This method helps in reducing the calculations and results in small numerical values. This method depends on estimating the mean and rounding to an easy value to calculate with. Again this value is subtracted from all the sample values. When the samples are converted into equal size ranges or class intervals, a central class is chosen, and the computations are performed.
Assumed Mean Method Formula
Let x1, x2, x3,…,xn are mid-points or class marks of n class intervals and f1, f2, f3, …, fn are the respective frequencies. The formula of the assumed mean method is:
Here,
a = assumed mean
fi = frequency of ith class
di = xi – a = deviation of ith class
Σfi = n = Total number of observations
xi = class mark = (upper class limit + lower class limit)/2
When working on a given set of data, it is not possible to remember all the values in that set. But we require inference of the data given to us. This problem is solved by mean median and mode. These, known as measures of central tendency, represent all the values of the data. As a result, they help us to draw an inference and an estimate of all the values. Let us learn about the measures of central tendency and the calculation of Mean Median and Mode.
As already discussed, the mean median and mode are known as measures of central tendency. They are also known as statistical averages. Their simple function is to mathematically represent all the values in a particular set of data. Hence, this representation shows the general trend and inclination of all the values.
An average provides a simple way of representation of all the individual data. It also aids in the comparison of different groups of data. In addition to this, an average in economic terms can represent the direction an economy is headed towards. Hence, it can be easily used to formulate policies and bring about a reform for a better economy.
For example, a low per capita income is an indication for the government to formulate policies focused on the increase in income of people. We will learn about three measures of central tendency- Mean Median and Mode.
Arithmetic Mean
The first concept to understand from Mean Median and Mode is Mean. Mean is simply defined as the ratio of the summation of all values to the number of items. Note that there are two types of the arithmetic mean which are simple arithmetic mean and weighted arithmetic mean.
Mean = ∑X ÷ N
Here, ∑X= Sum of all the individual values and N= Total number of items
The simple arithmetic mean considers all the values in data as equal and grants equal importance to each value. Whereas, in weighted arithmetic mean weights or importance is assigned to the values. Without further delay let us study methods of constructing mean.