**Numerical Data:**Numerical data is the information given with the help of numbers.

**Pictorial Representation or Graph of the Data:**The representation of numerical data through pictures or graphs is known as pictorial or graphical representation of data.

**Pictograph:**Pictograph is a pictorial representation of the gathered data.

**Bar Graph:**When data is represented in a figure form that resembles a bar, then it is called bar graph.

**Bar Graphs in Details**

When numerical data is represented in the form of a number of bars, then it is called bar graph or chart. The bars are of uniform width and erected horizontally or vertically. The bars are placed in equal distances from each other. As there are numerous bars to represent a large number of data, each bar represents only a particular value of the numerical data. If two bars represent data of different value, they are of different sizes. The horizontal bars are drawn on x-axis and the vertical lines which show the scale of height of the bars is the y-axis.

**Example**

Bar graphs or charts provide various advantages, like:

Bar graphs help a lot in easy representation of the data. A bar graph or a chart also helps in drawing a quick conclusion by having just a glance. For instance as in the following figure, a graphical figure would reflect the easy way to show government expenditures in different sectors. The y-axis represents the amount of money spent in million and the x-axis represents the different sectors. By looking at the bar graph, you can easily tell that government has spent the most in the Defense sector.

**Test**

Represent the number of government companies in different years by means of a bar graph.

Year | Number of companies |

2001 2002 2003 2004 | 80 120 140 180 |

**Pie chart in details**

In a particular area, the amount of wheat production for three consecutive years are 20 million in 2001, 25 million in 2002 and 55 million in 2003. When we represent the following figures in the form of a pie, chart, the degree of the angle to represent each of the quantity needs to be calculated.

For instance, the production of wheat:

2001 = 20 million tonnesTherefore, the total amount of wheat produced in these three years are, 20 + 25 + 55 = 100 million tonnes.

2002 = 25 million tonnes

2003 = 55 million tonnes

Let’s take 100 million tonnes = 360 degree

Therefore, 1 million tonne will be = 360/100

20 million tonne will be = 360/100 x 20 = 3.6 x 20 = 72 degree. (Applying Unitary method)

Similarly, 25 million tonne will be = 360/100 x 25 = 3.6 x 25 = 90 degrees. (by unitary method)

Similarly, 55 million tonne will be = 360/100 x 55 = 3.6 x 55 = 198 degrees.(by unitary method)

The best way to check the result, whether it is correct or not can be done by adding up the three quantities, 72 degree + 90 degree + 192 degree = 360 degree.

If the result of the sum is 360 degree, then most of the time your calculations are fine but in any case if the sum does not result to 360 degree then it is definitely wrong.

A pie chart also known as circle graph is a representation of a circle chart divided into sectors. The circle is divided into various parts and each part or each arc represents a value. The arc length is directly proportional to the quantity it represents. The total value of the data should be represented within 360 degrees because the pie chart is always a circle.

Pie charts are especially effective in places where there is a need to compare between various quantities. Pie charts are a very good analysis tool in case of journalism or business but it is not so effective in case of scientific literature. However, the particular form of pictorial representation of data is widely used and attractive too.

**Example**

In a survey which represents the percentage of intelligence in a class it is seen that 20% of the students are highly intelligent, 70% of the students are average and 10% are below standard. While analyzing the data, if it is represented in the form of a pie chart then it will be much easier to get a conclusion. The pie chart representing the above data will look like the following:

**Test**

Represent the following data in a pie chart which gives the number of staffs in different ages in a particular office, which has a total number of 60 staffs. 20 people are below 25 years of age, 30 people are between 25 to 50 age group and there are only 10 people above 50 years of age.

**Answer:**

By unitary method, we have to take total number of staffs as 360 degrees.

Therefore, 60 staffs represent = 360 degree

1 staff will represent = 360/60

20 staffs (below 25 years) will represent = 360/60 x 20 = 120 degrees

30 staffs (between 25-50 years) will represent = 360/60 x 30 = 180 degrees

10 staffs (above 50 years) will represent = 360/60 x 10 = 60 degrees

Therefore, number of staffs below 24 years of age will represent 120 degree.

Number of staffs between 25-50 years of age will represent 180 degree and number of staffs above 50 years of age will be 60 degree.

**Checking:**

Three quantities in degree calculated are 120 degree, 180 degree and 60 degree.

Sum of the quantities are 120 degree + 180 degree + 60 degree = 360 degree.

Therefore, the calculation is right.

Mean, Median, Mode

Mean

Mean or arithmetic mean refers to calculating the sum of all numbers in the set and then dividing the numbers by the number of quantities or members. It is very much helpful when you need to draw a summary out of a large collection of numbers. However, don't confuse mean with average as mean is only one of the several kinds of average.

The Median

Getting the median is as easy as getting the 'middle value' in a list of numbers. When you are given with a set of odd quantities, then you need to sort out those numbers into increasing order and find out the middle number. That middle number is the median. However, when you are given an even number of quantity, again you need to sort them out in increasing order. Then you need to find out the sum of the two middle numbers and divide it by two. The result is the median.

Mode

Finding the mode is very easy as all you need to do is to find out the number which occurs most in a given list of numbers. However, if a list contains no number, occurring more than once then that list has no mode. Range of a set of numbers is also easy as it needs you to calculate the difference between largest number and the smallest number of the list.

Example

**1)**Find the mean of the set {3,7,8}.

The first step is to add the three numbers that is, 3 + 7 + 8 = 18.

The value of the addition is 18.

No. of quantities in the set = 3.

Therefore, the mean is 18/3 = 6.

**2)**Find the median of the set {4, 2, 6, 12, 5}

The first step would be to sort them in increasing order that is, 2, 4, 5, 6, 12.

The middle number is 5.

With odd rule, the median is 5.

**3)**Find the median of the set {3, 5, 10, 6, 15, 11}

Sorting the set in increasing order, we get, 2, 4, 7, 5, 9, 11

The two middle numbers are 7 and 5.

Sum of those two numbers = 7 + 5= 12.

Dividing the value by 2, we get, 12/2 = 6.

Therefore the median is 6.

**4)**Get the mode from the set {2, 9, 3, 9, 2, 6, 12, 9}

Sorting the numbers we get, 2, 2, 3, 6, 9, 9, 9,12…

9 is the mode as it has appeared the most number of times.

**5)**Calculate the range of the set {3, 5, 29, 14, 9, 11}

The largest number in the set is 29 and the smallest number is 3.

Therefore, the difference is 29 – 3 = 26.

The range is 26.

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