Graphical Representation Solutions for ICSE Board Class 10 Mathematics

ICSE

Graphical Representation Solutions for ICSE Board Class 10 Mathematics

(Histograms, Frequency Polygon and Ogives) Solutions for ICSE Board Class 10 Mathematics (Concise - Selina Publishers)

Free download of step by step solutions for class 10 mathematics chapter 23 - Graphical Representation (Histograms, Frequency Polygon and Ogives) of ICSE Board (Concise - Selina Publishers). All exercise questions are solved & explained by an expert teacher and as per ICSE board guidelines

(Histograms, Frequency Polygon and Ogives) Solutions for ICSE Board Class 10

Histogram

A histogram is made up of adjacent (contiguous) boxes. It has two axes, one vertical and one horizontal. The data is represented on the horizontal axis, which is labelled (for instance, distance from your home to school). The frequency or relative frequency axis is labelled on the vertical axis (or per cent frequency or probability). With any label, the graph will have the same form. The histogram, like the stemplot, can show you the form of the data, as well as its centre and spread.

Frequency Polygons

Frequency polygons are similar to line graphs in that they make continuous data visually easy to interpret, much as line graphs do.

To construct a frequency polygon, first look over the data and decide how many intervals, or class intervals, to use on the x and y axes. Begin graphing the data points after selecting the necessary ranges. Draw line segments to connect the points when they've all been plotted.

Ogives

In architecture, the term "ogive" is used to denote curves or curved shapes. Ogives are graphs that are used to estimate the number of numbers that are below or above a given variable or value in data. To create an Ogive, first, use a frequency table to calculate the cumulative frequency of the variables. It's accomplished by summing the frequencies of all of the previous variables in the data set.

FAQs on Graphical Representation Solutions for ICSE Board Class 10 Mathematics

1. What is the cumulative frequency?

Another useful piece of data is the number of data points that fall below a specific class border. A teacher, for example, would want to know how many children scored below 80%, a doctor might want to know how many individuals have cholesterol below 160, or a store manager might want to know how many stores make less than $2000 per day. A cumulative frequency is what this is called. This would be a cumulative relative frequency if you wanted to know what percentage of the data falls below a given class border. You are looking for how many data values fall below the upper-class limit with cumulative frequencies. To acquire more knowledge on the subject, you can click on Graphical Representation Solutions for ICSE Board Class 10 Mathematics.

2. What are the benefits of histograms?

Histograms can reveal the typical distribution of a process that is going smoothly over time. Any fluctuation is immediately observed when histograms are produced regularly. This is an impactful benefit for businesses since it allows them to immediately identify and address process variance. A normal distribution is commonly indicated by a bell-shaped curve in the bar graph. The variation that should be addressed is shown by spikes in the graph. Spikes like these might also signal opportunities to profit from a trend.

3. How can histograms be used in real life?

To figure out how many customers come into a restaurant at different times throughout the day, restaurant managers may create a histogram. The vertical axis represents the number of patrons, and the horizontal axis represents the time intervals. The graph would display the frequency distribution of when customers arrive at the restaurant (25 come in at 9 a.m.; 77 at noon, etc.). Managers can identify strategies to profit from greater traffic if large spikes are observed at specific periods of the day (speciality items, pricing adjustments).

4. How is frequency polygon better than histogram?

A histogram and a frequency polygon have a lot in common. The only variation is in the way the graph is constructed. A frequency polygon is created by drawing a point to represent the frequency of one interval and connecting it to the point representing the frequency of the next interval. A histogram is made up of bins with a width that represents the interval and a height that represents the number of data points in each interval.

The major function of a frequency polygon is to allow the depiction of two sets of data in a histogram-like manner on the same graph. Two histograms on the same graph tend to obscure each other, making the comparison more difficult; however, two frequency polygons can be graphed together with far less interference.

5. How to prepare for graphical representation - Histogram, Frequency Polygon and Ogives?

To prepare for Graphical representation - Histogram, Frequency Polygon and Ogives for Class X ICSE, it is quite important to be thorough with all the basics of a graph. Without knowledge about basic bars and graphs, it is next to impossible to understand histogram, frequency polygon and ogives. It would also be helpful to learn about how graphical representation is applied in real life. To strive towards perfection with regards to this topic, it is important to practice. To practice, you can solve sample papers related to this topic. In the Vedantu app and website, you can gain access to free study materials.