Graphing Data in Grade VII

Hello friends! Today we will discuss two interesting topics of algebra that you study in grade VII. The first topic that we will cover today is Graphing data to demonstrate relationships and the next will Arithmetic sequence. Graphing is a simple pictorial representation of any data on the number line. With the help of graph you can easily understand and easily analyze the data.  Data recorded in experiments or surveys is exhibited by a statistical data graph. We use different variant types of graphs for the representation of the statistical data graph. Mainly, we have eleven types of graphs that we generally use for the representation of the statistical data.

1. Box Plot: It is a convenient way of graphical representation of data or we can say it is a way of summarizing a set of data measured on an interval scale. It is sometimes used for the exploratory data analysis.  In box plot graph we show the shape of the distribution, its central value, and variability.
2. Stem and leaf plot: this is a method used for showing the frequency with which certain classes of values occur. In this we can make a frequency distribution table or a histogram for the values, or we can easily use a stem-and-leaf plot graph method.
3. Frequency polygon: it is a graphical display of a frequency table, in this intervals are shown on the X- axis and the number of scores in each interval is represented by the height of a point situated above the middle interval. The points are connected in such a way that together with the X-axis they form a polygon.

 

1. Scatter plot: it is a graph in which we use Cartesian coordinates to display values for two variables for a set of data. The data is represented as a collection of pints, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis.   
2. Line graph: this type of graph displaying data or information that changes continuously over time.

 

 

1. Bar graph: A bar chart or bar graph is a graph with rectangular bars with lengths proportional to the different values that they represent. The bar graph can be plotted on horizontal axis or on vertical axis.

1. Histogram: it is a graphical representation of data that shows a visual impression of the distribution of data.

 

1. Pictograph: They are often used for the representation of the data in graphical form.
2. Map graph: This type of graph is also called as the grid system. in this is the standard grid of up and down drawn lines and left and right drawn lines creating a grid of intersecting lines.

 

1. Pie graph: The pie graph is the most commonly used statistical charts for the representation of the business data and the mass media data.

 

1. Line plot: it is a graph that shows frequency of data along a number line. It is one of the best way for the representation of the data.

 

 

 

In Grade VII, students learn histo graphical representation of the data, frequency polygon and the bar graphs. In Statistical data graph, a histogram is used for the representation of the two dimensional data used to graph continuous data. Histograms do not have spaces between the bars.

Here is an example in which you see how to represent data in form of histogram graph.

 

.

Data	Frequency
0-10	5600
10-20	5250
20-30	4750
30-40	3750
40-50	3500
50-60	2750
60-70	2600
70-80	2750
80-90	2500
90-100	2400

Next method is frequency polygon, in this we use to study the graphical representation of a frequency table. This type of graph offers approximate smooth bend that explains a frequency distribution if the class intervals were to be made as small as possible.

The study of points is involved so that collectively with the X-axis they form a polygon.

Statistical data graph in Frequency polygon problem:

Construct the Statistical data graph using Frequency polygon.

Data	Mid term value	Frequency
0-2	1	1
2-4	3	12
4-6	5	9
6-8	7	1
8-10	9	1

Graph:

 

Data Graphs Using Bar Graph

Other graphs that you study in the same class is called as bar graph as I already mentioned earlier in the article that what it is? Let’s take an example of this, and see how to plot such kind of graph.  These graphs are one of the most interesting topic that you can easily plot.

 

Here is an example of construction of bar graph for the statistical data graph.

Brain region	Receptor Binding
1	35
2	50
3	28
4	20

Graph:

 

This is all about the different types of graph that you use for the demonstration of the data. Now, we will switch to the next topic that is Arithmetic sequence. It is also known as the arithmetic progression, or arithmetic series. An arithmetic sequence consists of the sequence of numbers and accept the first term,  remaining terms can be obtained by adding one number to its preceding number. It is denoted as the arrangement of two consecutive numbers, the progression which is constant.  Other than AP we also have other type of series called as geometric progression, harmonic progression. You will learn all these in the future grades.

 

 

Arithmetic progression also have its own general form, if you see any such type of equation then understand that it is in form of A.P. The general form of an A.P. is given as:

 

a = first term, d = common difference, then A.P. is a, a+d, a+2d, a+3d,.....

In this every time you will observe that in any term the coefficient of d is always less by one than the number of terms in the series.

Thus, second term is a+d

third term is a+2d

fourth term is a+3d

tenth term is a+9d

and generally, n^th term is a + (n-1)d.

If n is the number of terms and if t_n is the n^th term, then t_n = a+(n-1)d.

 

 

In arithmetic progression common difference is calculated by subtracting any term from the series from the intermediate succeeding them.  Let’s see few examples of the arithmetic series.  

See the following series and find whether it is a A.P. or not?

i) 1, 3, 5, 7, …

In this example, common difference in the first sequence is 2 and each term in the first sequence is succeeding with the increment of the two and thus forming an arithmetic sequence.

ii) 3, 7, 11, 15, …

In this there is difference of 4, in all the terms present in the series. You can easily found the nth term by adding 4 in the n-1th term.

iii) 15, 12, 9, …

This is also in form of arithmetic progression; in this each term is decreasing by 3.

iv) x, x - d, x - 2d, .....

in the fourth it is -d

v) p , p + q, p + 2q, p + 3q,..

In this each time there is increment of q. so the series is in form of A.P.

We can also calculate the sum of the Arithmetic progression. The sum is some sort similar to normal addition, let’s have a look on how to do addition of the arithmetic sequences.

Let a=first term, d=common difference, l=t_n=last term, s=required sum. Then,

S= a + (a +d) + (a + 2d) +(a + 3d)+…..a + (n -2)d + a+(n-1)d

If we write the same series in the reverse order then we will get the sequence as:

 

S= a +(n- 1)d+ a+(n - 2)d+….+ a + d +a

Adding together the two series we will get the answer as:

2s = [2a +(n-1)d] + [2a + (n-1)d] +………up to nth term.

2s = n2a + (n -1),

S = n/2 2a + (n -1)d,

S = n/2a + a+(n-1)d

 

S = n/2(a +1),

Here, l = a + (n -1)d

 

Now have a look on the properties of the Arithmetic progression.

 

If p, q, r, s are in A.P., then

1: p +- k, q +- k, r +- k, s +- k,… are also in arithmetic progression.

2: kp, kq, kr, ks…. will also be in A.P.

 

 

A remark on finding a few members of an A.P. whose sum is given along with other conditions:

1. If the sum of three numbers in A.P. is given, take the numbers as a-d, a, a+d.
2. For the five number series always take take them as: a – 2d, a –d, a,  a+d, a +2d.
3. If you have to take a four numbers series then always take them as: a- 3d, a – d, a +d, a + 3d.
4. For any six term, take the series as: a – 5d, a – 3d, a – d, a+ d, a +3d, a +5d.

This is all about arithmetic progression. Using the above mentioned form, series, formula and properties you can easily solve different type of arithmetic progression problems.