Statistics homework answers

Statistics is the branch of applied mathematics which deals with scientific analysis of data. The subject statistics had been started in early days as arithmetic to aid a ruler who needed to know the wealth of his subjects to levy new taxes. Now a days statistics  plays an important role in all organizations in their decision-making and planning. Statistics homework deals with mean,median and mode.

Classification of Statistics Homework Answers:

In statistics homework answers has following topics are

• Arithmetic mean
• Median
• Mode

The arithmetic mean;

In Statistics the arithmetic mean (A.M) or simply the mean or average of n observations x1, x2, …, xn is defined to be number x such that the sum of the deviations of the observations from x is 0.

         x1 +x2 +x3.......xn
x =  --------------------
                     n

the symbol Σ, called sigma notation is used to represent summation.

x=Σ xi
   -------
      n

Homework Example:

Calculate  mean of the data 9, 11, 13, 15, 17, 19.

Sol :

X =   Σxi/n = `[9+11+13+15+17+19]/[6] ` =` [14]/[6]`

Median :

Median is defined as central most or middle value for given series of data it should be arranged in ascending or descending order.

Homework Example:

Find the median of 23, 25, 29, 30, 39.

Sol:

The given values are already in  ascending order. No. of observations N = 5.

So the median = ` (N+1)/(2)`  =`(5+1)/(2)`
= 3 rd term =29
∴ Median = 29.

Mode:

In Statistics answers,Mode is also a measure of central tendency.

In a set of each observations, mode is defined as value which occurs most often.

If the data are arranged in the form of a frequency table, the class corresponding to  greatest frequency is called  modal class.

Homework Example:

Find the mode of 7, 4, 5, 1, 7, 3, 4, 6,7.

Sol:

Arranging the data in  ascending order, we get 1, 3, 4, 4, 5, 6, 7, 7, 7.

In above data 7 occurs several times. Hence mode = 7.

Homework Problems and Answers for Statistics:

Calculate mean :    
Problem 1:
Calculate the mean of the data 7, 12, 18, 14, 19, 20.
Problem 2:
Calculate the mean of the data   16,18,14,15,21,30,26,44
Problem 3: 
Calculate the mean of the data   22,77,55,11,22,26,38,72
Answers:
1) 15
2) 23
3) 40.35

Calculate median:
Problem 1: 
Find the median of 3, 4, 10, 12, 27, 32, 41, 49, 50, 55, 60, 63, 71, 75, 80.
Problem 2:
Find the median of 29, 23, 25, 29, 30, 25, 28.
Problem 3: 
Find the median of 26, 25, 29, 23, 25, 29, 30, 25, 28, 30.
Answers:
1) 49
2) 28
3) 27

Calculate mode:
Problem 1:
Find the mode of 12, 15, 11, 12, 19, 15, 24, 27, 20, 12, 19, 15
Problem 2:
Find the mode of 3,5,8,3,9,3
Problem 3: 
Find the mode of 3,5,8,5,6,7
Answers:
1) 12 and 15
2) 3
3) 5
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