Chapter 3 Cumulative Review Algebra 2 14 Questions
The give-and-take Ogive is a term used in architecture to describe curves or curved shapes. Ogives are graphs that are used to estimate how many numbers lie below or above a particular variable or value in data. To construct an Ogive, firstly, the cumulative frequency of the variables is calculated using a frequency table. Information technology is washed by adding the frequencies of all the previous variables in the given data set. The result or the terminal number in the cumulative frequency tabular array is ever equal to the total frequencies of the variables. The most ordinarily used graphs of the frequency distribution are histogram, frequency polygon, frequency curve, Ogives (cumulative frequency curves). Allow united states of america discuss 1 of the graphs chosen "Ogive" in detail. Here, we are going to have a look at what is an Ogive, graph, chart and an example in detail.
Ogive Definition
The Ogive is divers equally the frequency distribution graph of a series. The Ogive is a graph of a cumulative distribution, which explains data values on the horizontal plane axis and either the cumulative relative frequencies, the cumulative frequencies or cumulative per cent frequencies on the vertical axis.
Cumulative frequency is divers equally the sum of all the previous frequencies upwardly to the electric current point. To find the popularity of the given information or the likelihood of the information that fall within the certain frequency range, Ogive curve helps in finding those details accurately.
Create the Ogive past plotting the point respective to the cumulative frequency of each grade interval. Virtually of the Statisticians use Ogive curve, to illustrate the data in the pictorial representation. It helps in estimating the number of observations which are less than or equal to the particular value.
Ogive Graph
The graphs of the frequency distribution are frequency graphs that are used to showroom the characteristics of discrete and continuous data. Such figures are more appealing to the middle than the tabulated data. It helps united states to facilitate the comparative report of ii or more frequency distributions. We tin can relate the shape and pattern of the 2 frequency distributions.
The two methods of Ogives are:
- Less than Ogive
- Greater than or more than Ogive
The graph given above represents less than and the greater than Ogive curve. The ascent bend (Brownish Curve) represents the less than Ogive, and the falling curve (Greenish Curve) represents the greater than Ogive.
Less than Ogive
The frequencies of all preceding classes are added to the frequency of a class. This series is chosen the less than cumulative serial. It is constructed by calculation the first-grade frequency to the 2d-grade frequency and then to the third class frequency and so on. The downwardly cumulation results in the less than cumulative series.
Greater than or More than Ogive
The frequencies of the succeeding classes are added to the frequency of a class. This serial is called the more than or greater than cumulative series. Information technology is constructed past subtracting the starting time class, second course frequency from the total, 3rd class frequency from that and so on. The upward cumulation result is greater than or more than the cumulative series.
Ogive Chart
An Ogive Chart is a bend of the cumulative frequency distribution or cumulative relative frequency distribution. For drawing such a curve, the frequencies must be expressed as a per centum of the total frequency. So, such percentages are cumulated and plotted, equally in the instance of an Ogive. Below are the steps to construct the less than and greater than Ogive.
How to Draw Less Than Ogive Bend?
- Depict and marking the horizontal and vertical axes.
- Take the cumulative frequencies along the y-axis (vertical axis) and the upper-grade limits on the x-centrality (horizontal axis).
- Against each upper-class limit, plot the cumulative frequencies.
- Connect the points with a continuous curve.
How to Draw Greater than or More than Ogive Bend?
- Depict and mark the horizontal and vertical axes.
- Take the cumulative frequencies along the y-axis (vertical axis) and the lower-class limits on the 10-axis (horizontal axis).
- Confronting each lower-class limit, plot the cumulative frequencies.
- Connect the points with a continuous curve.
Uses of Ogive Curve
Ogive Graph or the cumulative frequency graphs are used to find the median of the given set of data. If both, less than and greater than, cumulative frequency bend is drawn on the same graph, we can easily observe the median value. The point in which, both the curve intersects, corresponding to the ten-axis, gives the median value. Apart from finding the medians, Ogives are used in computing the percentiles of the data set values.
Ogive Example
Question ane:
Construct the more than cumulative frequency table and draw the Ogive for the below-given information.
| Marks | 1-10 | 11-twenty | 21-xxx | 31-xl | 41-50 | 51-lx | 61-70 | 71-lxxx |
| Frequency | iii | viii | 12 | 14 | ten | 6 | 5 | 2 |
Solution:
"More than than" Cumulative Frequency Tabular array:
| Marks | Frequency | More than Cumulative Frequency |
| More than 1 | three | 60 |
| More than than 11 | 8 | 57 |
| More than than 21 | 12 | 49 |
| More than 31 | 14 | 37 |
| More than 41 | ten | 23 |
| More than than 51 | vi | 13 |
| More than 61 | 5 | 7 |
| More than than 71 | 2 | 2 |
Plotting an Ogive:
Plot the points with coordinates such as (70.five, 2), (60.v, vii), (50.5, 13), (40.v, 23), (30.5, 37), (20.5, 49), (10.5, 57), (0.5, lx).
An Ogive is connected to a betoken on the x-axis, that represents the bodily upper limit of the concluding class, i.e.,( 80.5, 0)
Accept 10-axis, 1 cm = 10 marks
Y-axis = ane cm – x c.f
More the Ogive Curve:
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