Thursday, May 15, 2014

statistics home work help

Statistics and its applications
 
The scientific methods of collection of data, its classification and application to commerce and everyday life is called statistics. A list of some important terms as follows:
  • ungrouped data 

  •  tabulation of data

  •  Range: the difference between maximum and minimum value in a given set.

  •  frequency

  •  frequency distribution

  • Mean : Sum of all the events divided by the total number of events

  • Median: The Median is the 'middle value' in your list

  • Average is the same as mean in statistics

  • Mode : The mode in a list of numbers refers to the number that occur most frequently
 
 

EXAMPLES

Example 1
 
Given a table of debtors and creditors, comment on the growth of the company.
 
Year
Debtors
Creditors
2000
10
15
2001
4
8
2002
7
9
2003
11
14
2004
16
20
2005
17
14
2006
12
13
 
Answer : Sundry creditors are more than the sundry debtors. Hence, the company’s growth is very slow and declining.   
 
 

Example 2
 
In the above table, find out the average number of debtors the company has.

Answer

Average/ Mean = Sum of total number of debtors/ total number of years

 = 77/7 = 11 debtors in an average for the years from 2000 through 2006
 
 

Example 3      

 
Find the median of the above table of creditors.

Answer

Step 1 given numbers in the creditors list: 15, 8, 9, 14, 20, 14 and 13

Step 2 Arrange numbers in increasing order: 8, 9, 13, 14, 14, 15 and 20

Step 3 Count the number of terms, it is 7

Step 4 the median here is the middle number = 14
 
 

Example 4      

 
Find the mode of the above table of debtors and creditors.

Answer

Mode is the value that occurs most frequently.

In the creditors list, 14 occurs twice while other values occur once hence 14 is the mode.
 

Try these questions
1.John wants to know how long he can dance without stopping, and decides to record how long he can dance (in minutes). The following is a graph he made to record the data. Based on the data, answer questions 1 and 2.
 
 
  1. Find the longest time period for which he danced.

    A. 15
    B. 25
    C. 30
    D. 20
    2. Answer B

    Solution

    It is the bar with maximum height.



  2. Find the average time for which he can dance.

    A. 15.7 minutes
    B. 20 minutes
    C. 15 minutes
    D. 17.5 minutes

    3. Answer A

    Solution

    Average = (10 + 5 + 15 + 20 +25 + 20 + 15)/7 = 15.7 minutes approx.



  3. Mean for the numbers 2, 3, 4, 5, 6, 1 is ------------.

    4. A. 2.8
    B. 3.5
    C. 4.6
    D. 5.4

    Answer B

    Solution

    Add all the numbers and divide it by 6

    Mean = 3.5


  4. The range of numbers 12, 23, 45, 67, 78, 89 is ----------.

    A. 65
    B. 77
    C. 87
    D. 98

    5. Answer B

    Solution

    Range = maximum value – minimum value
    =89 – 12 =77



  5. Find the median of: 23, 53, 32, 77, 87, 98, 12, 54, 76, and 53

    A. 54
    B. 53
    C. 53.5
    D. 55
    6. Answer C

    Solution

    Step 1:  Arrange numbers: 12, 23, 32, 53, 53, 54, 76, 77, 87, 98

    Step 2: Since there are even number of events, median will be 


    = (5th number + 6th number)/2

    =(53 +54)/2 = 107/2 = 53.5



  6. Find the mode for the above sequence.

    A. 53
    B. 23
    C. 45
    D. 40

    7. Answer A

    Solution

     53, as it is repeated twice.



  7. Find the mean in the above sequence.

    A. 56.5
    B. 45.5
    C. 34.4
    D. 30.5


    Answer A

    Solution

    Step 1:  Add all the numbers = 565

    Step 2:   Divide it by the total numbers = 10

    Step 3:  The mean is 56.5
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