Step by step math solution

Line Plot Graph made simple
Line Plot Definition
A data represented on a number line with marks like ‘x’ or any other mark which shows the frequency of a value in the data is defined as the line plot. For example:
The line plot below shows the marks of 20 pupils in a class.

The ‘x’ marks show the frequency of the marks obtained by the pupils
Let us now take a quick look at how to make a line plot
• First we need to gather the information. Once the information is ready we look for the data sets which occur often that is the data which is frequently shown. Something like the favorite flavor of certain people or the number of pets a group of people have.
• The data is to be sorted and then a chart is created so as to organize the list. We then name the chart for convenience.
• This is an important step which involves determining the scale. The scale might not have the labels that are not the data values as per the given information and hence we need  to decide the scale depending upon the frequency of the data items for which a numerical scale is used which begins with the least number and ends in the highest number in the data set.
• Now we draw a horizontal line which is similar to  a number line according to the chosen scale.
• Finally we start marking ‘x’ above the line corresponding to the number on the scale as per the data we have. Once the markings are done, the line plot for the given data is ready for further analysis.

Let us now make line plot graphs using a line plot example
Given are the costs of 15 books sold in a book store, represent a data as a line plot graph.
$20 $15 $9 $15 $9 $20 $9 $20 $20 $35 $25 $20 $9 $30 $15
We need to decide on the scale, the lowest value is 9 and the highest value is 35. So, the scale should start from 5 and end in 35

Solve by the addition method

Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign (+). For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples. Therefore, 3 + 2 = 5. (Source: Wikipedia)

Example Problems for Solve by the Addition Method:-

Problem 1:-

Solve 453 + 213 by the Addition method.

Solution:-

In the following step by step process of addition method

Step 1:-

               453
            + 213
           -----------
           -----------
The above equation 453 is adding to 213 in between (+) plus operation. In basic addition process start with right side value to left side value

Step 2:-

               453
            + 213
           -----------
                   6
           -----------
Adding the right side values 3 and 3. 3 is equal with 3 in 3+3 =6. Then move to next value.

Step 3:-

               453
            + 213
           -----------
                 66
           -----------
Adding the next two values 5 and 1. 5 adding with value 1 in 5+1 =6. Then move to next value.

Step 4:-

               453
            + 213
           -----------
               666
           -----------

Adding the last two values 4 and 2. 4 adding with value 2 in 4+2=6. We get the final answer is 666.

Problem 2:-

Solve 654 + 323 by the Addition method.

Solution:-

In the following step by step process of addition method

Step 1:-

               654
            + 323
           -----------
           -----------

The above equation 654 is adding to 323 in between (+) plus operation. In basic addition process start with right side value to left side value

Step 2:-

               654
            + 323
           -----------
                   7
           -----------

Adding the right side values 4 and 3. 4 adding with value 3 in 4+3 =7. Then move to next value.

Step 3:-

               654
            + 323
           -----------
                  77
           -----------

Adding the next two values 5 and 2. 5 adding with value 2 in 5+2 =7. Then move to next value.

Step 4:-

               654
            + 323
           -----------
               977
           -----------

Adding the last two values 6 and 3. 6 adding with value 3 in 6+3=9. We get the final answer is 977.


Practice Problems for Solve by the Addition Method:-

Problem 1:-

solve 421 + 167 by the addition method.

Answer:- 588

Problem 2:-

solve 217 +171 by the addition method.

Answer:- 388

Problem 3:-

solve 383 + 71 by the addition method.

Answer:- 454

Problem 4:-

solve 152 + 38 by the addition method

Answer:- 190

Problem 5:-

solve 43 + 24 by the addition method.

Answer:- 67

Frequency Distribution in Statistics

In mathematics frequency distribution is used in statistics. Mean of a frequency distribution is that the arrangement in which sets of value occurs and in the values one or more variable takes place. Frequency distribution is in the form of either graphical or tabular. Each value in the table contains frequency or count of values, how many times they occur. The values of frequency in group or interval forms.  After summarizing the entire values frequency distribution table is formed. Mean of frequency distribution is also that it shows the total number of observations within a given interval. The interval is either exclusive or exhaustive. The size of intervals generally depends on the data which we have to analyze and calculate. One thing we have to remind that the intervals must not be overlapped to each other.

Now we discuss that how to construct frequency distribution tables. We use some steps to make a frequency distribution table. In step one; we determine the range of given data. Range of given data means the difference between the higher value and the lower value. In step two, we decide that which data can be grouped means formulation of approximate number of groups. There are no particular rules for step two. It can be 5 groups to 15 groups. But there is one formula for this (K=1+3.322logN), where K is the no of groups, logN is the total number of observations.

In step third, we decide the size of intervals.  The size of interval is denoted by (h). To determine the size we can use a formula (h= range/number of groups). If result is in fraction then we choose next higher value. In step fourth, we decide start point means starting from the lowest value and in the ascending order. In step fifth, we determine the remaining groups. It is determined by adding the interval size corresponding to all values. In step sixth, we distribute all the data into their groups. For this we use tally marks method because it is suitable for tabulating the observations into their respective groups. By using these six steps we can construct a frequency distribution table.

Now we come to standard deviation for frequency distribution. It is a measure of variation or measure of dispersion amongst the data. In place of taking absolute deviation we may square each deviation and obtained the variance. The square root value of variance is known as standard deviation for given values of frequency.