OP Malhotra Class-11 Statistics S.Chand ISC Maths Solution Chapter-28. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-28 (a), 28 (b), 28 (c), 28 (d), With Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.
OP Malhotra Class-11 Statistics S.Chand ISC Maths Solution
| Class: | 11th |
| Subject: | Mathematics |
| Chapter : | Ch-28 Statistics of Section -C |
| Board | ISC |
| Writer | OP Malhotra |
| Publications | S.Chand Publications 2020-21 |
–: Select Topics :-
OP Malhotra Class-11 Statistics S.Chand ISC Maths Solution
Measures of Dispersion
The dispersion or scatter in the data is measured based on the observations and the types of the measure of central tendency. The different types of measures of dispersion are:
- Range
- Quartile deviation
- Mean deviation
- Standard deviation.
In Class 11 statistics, you get a clear knowledge of all the measures of dispersion except quartile deviation, which will be studied in your higher classes.
Range
The range is the difference between the maximum value and the minimum value
Range = Maximum Value – Minimum Value
Mean Deviation:
Mean deviation is the basic measure of deviations from value, and the value is generally a mean value or a median value. In order to find out the mean deviation, first take the mean of deviation for the observations from value is d = x – a Here x is the observation, and a is the fixed value.
The basic formula to find out the mean deviation is
Mean Deviation = Sum of absolute values of deviations from ‘a’ / Number of observations
Mean Deviation for Ungrouped Data:
Calculation of mean deviation for ungrouped data involves the following steps :
Let us assume the observations x1, x2, x3, …..xn
Step 1: Calculate the central tendency measures about to find the mean deviation and let it be ‘a’.
Step 2: Find the deviation of xi from a, i.e., x1 – a, x2– a, x3 – a,. . . , xn– a
Step 3: Find the absolute values of the deviations, i.e., | x1 – a |, | x2– a |, |x3 – a|,. . . ,|xn– a| and the drop the minus sign (–), if it is there,
Mean Deviation for Grouped Data:
The data can be grouped into two ways namely,
- Discrete frequency distribution
- Continuous frequency distribution
The methods of finding the mean deviation for both the types are given below
Discrete Frequency Distribution
Here, the given data consist of n distinct values x1, x2, x3,….xn has frequencies f1, f2, f3,….fn respectively. This data is represented in the tabular form as and is called discrete frequency distribution, and the data are given below
| x | x1 | x2 | x3 | …… | xn |
| f | f1 | f2 | f3 | …… | fn |
Mean Deviation About Median:
To find the mean deviation about median for the given discrete frequency distribution. First arrange the observation in ascending order to get cumulative frequency which is equal or greater than N/2, where N is the sum of the frequencies.
Exe-28 (a)
OP Malhotra Class-11 Statistics S.Chand ISC Maths Solution
Page 28-3 to 28-4
Question 1:
On set of 100 observation has …………….. sets of given observation.
Question 2:
……………………
……………………..
……………………..
Question 7:
The mean and standard deviation of distribution of 100 ……………….. 250 stems lakes together.
Exe-28 (b)
OP Malhotra Class-11 Statistics S.Chand ISC Maths Solution
Page 28-16 to 28-18
Question 1:
Find the median of following sets of data:
(i)……………….
(ii)…………….
………………….
Question 2:
……………………..
………………………
……………………..
Question 21:
Find the interquartile range, semi ………… frequency distribution.
Exe-28 (c)
OP Malhotra Class-11 Statistics S.Chand ISC Maths Solution
Page 28-22 to 28-23
Question 1:
Find the mode of the following data:
(i)…………
(ii)………..
(iii)…………
(iv)…………..
Question 2:
…………………….
…………………….
…………………….
Question 12:
Find median, mean and mode marks and determine the limit between which 80% of the student have secured marks.
……………………
Exe-28 (d)
OP Malhotra Class-11 Statistics S.Chand ISC Maths Solution
Page 28-25 to 28-26
Question 1:
Find the mode of the given distribution by drawing a histrogram.
…………………..
Question 2:
……………………
…………………….
……………………..
Question 8:
(i) In an symmetrical ……………. the mode.
(ii) f mode in a …………………. probable mean.
(iii) Find the median …………. and mode 36.
Chapter Test
OP Malhotra Class-11 Statistics S.Chand ISC Maths Solution
Page 28-27 to 28-28
Question 1:
The mean of two sets of sizes 40 & 60 ……………… together.
Question 2:
…………………..
…………………..
…………………..
Question 10:
Graphically find the mode of following distribution :
…………………
-: End of Statistics Solution :-
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