# Statistics: Class 10 Mathematics NCERT Chapter 14

## Key Features of NCERT Material for Class 10 Mathematics Chapter 14 – Statistics

In the last chapter 13, you learned about surface areas and volumes. In this chapter, you will learn about Statistics.

#### Ungrouped Data

Ungrouped data will be data in its unique or crude structure. The observations are not classified into gatherings.

For instance, the ages of everybody present in a classroom of kindergarten kids with the educator is as per the following:

3, 3, 4, 3, 5, 4, 3, 3, 4, 3, 3, 3, 3, 4, 3, 27.

This data shows that there is one grown-up present in this class and that is the educator. Ungrouped data is anything but difficult to work when the data set is little.

#### Grouped Data

In grouped data, observations are sorted out in gatherings.

For instance, a class of students got various grades in a school test. The data is arranged as follows:

This shows what number of students got the specific grades. Grouped data is simpler to work with when a lot of data is available.

#### Frequency

Frequency is the occasion when a specific observation happens in data.

#### Class Interval

Data can be grouped into class intervals with the end goal that all observations in that range have a place with that class.

Class width is equal to upper class limit– lower class limit

#### Cumulative Frequency

Cumulative frequency is gotten by adding all the frequencies in a specific way.

Cumulative Frequency distribution of lesser than type

Cumulative frequency of lesser than type demonstrates the quantity of observations which are not exactly or equivalent to a specific observation.

Cumulative Frequency distribution of more than type

Cumulative frequency of more than type demonstrates the quantity of observations which are more prominent than or equivalent to a specific observation.

MEAN (AVERAGE): Mean [Ungrouped Data] – Mean of n observations, x1, x2, x3 … xn, is

MEAN [Grouped Data]: The mean for grouped data can be found by the accompanying three strategies:

(I) Direct Mean Method:

Class Mark =

Note: Frequency of a class is focused at its mid-point called class mark.

(ii) Assumed Mean Method: In this, a subjective mean ‘a’ is picked which is called, ‘accepted mean’, some place in all the estimations of x.

… [where di = (xi – a)]

(iii) Step Deviation Method:

… .. [where , where h is a typical divisor of di]

MEDIAN: Median is a proportion of central propensity which gives the estimation of the center most observation in the data.

… where[l = Lower breaking point of median class; n = Number of observations; f = Frequency of median class; c.f. = Cumulative frequency of going before class; h = Class size]

(iii) Showing a cumulative frequency distribution graphically as a cumulative frequency curve, or an ogive of the lesser than type and of the more than type. The median of grouped data can be gotten graphically as the x-coordinate of the point of intersection of the two ogives for this data.

Significant relations between strategies for discovering mean

• Every one of the three techniques for discovering mean yield a similar outcome.
• Step deviation strategy is simpler to apply if all the deviations have a typical factor.
• Assumed mean technique and step deviation strategy are simplified adaptations of the direct technique.

#### Mode:

(I) Ungrouped Data: The estimation of the observation having the most extreme frequency is the mode.

(ii) Grouped Data

… where[l = Lower breaking point of modal class; f1 = Frequency of modal class; f0 = Frequency of the class going before the modal class; f2 = Frequency of the class after the modal class; h = Size of class interval. c.f. = Cumulative frequency of going before class; h = Class size]

Mode = 3 Median – 2 Mean

October 26, 2020