Class 9 Exam  >  Class 9 Notes  >  RD Sharma Solutions for Class 9 Mathematics  >  RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics PDF Download

Find the median of the following data :

Q1 . 83 , 37 , 70 , 29 , 45 , 63 , 41 , 70 , 34 , 54

SOLUTION :

Numbers are 83 , 37 , 70 , 29 , 45 , 63 , 41 , 70 , 34 , 54

Arranging the numbers in ascending order

29 , 34 , 37 , 41 , 45 , 54 , 63 , 70 , 70 , 83

n = 10(even)

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics
RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q2 . 133 , 73 , 89 , 108 , 94 , 104 , 94 , 85 , 100 , 120

SOLUTION :

Numbers are 133 , 73 , 89 , 108 , 94 , 104 , 94 , 85 , 100 , 120

Arranging the numbers in ascending order

73 , 85 , 89 ,94 ,  94 , 100 , 104 , 108 , 120 , 133

n = 10(even)

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics
RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q3. 31 , 38 , 27 , 28 , 36 , 25 , 35 , 40

SOLUTION :

Numbers are 31 , 38 , 27 , 28 , 36 , 25 , 35 , 40

Arranging the numbers in ascending order

25 , 27 , 28 , 31 , 35 , 36 , 38 , 40

n = 8(even)

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics
RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics


Q4 . 15 , 6 , 16 , 8 , 22 , 21 , 9 , 18 , 25

SOLUTION :

Numbers are 15 , 6 , 16 , 8 , 22 , 21 , 9 , 18 , 25

Arranging the numbers in ascending order

6 , 8 , 9 , 15 , 16 , 21 , 22 , 25

n = 9 (odd)

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q5 . 41 , 43 , 127 , 99 , 71 , 92 , 71 , 58 , 57

SOLUTION :

Numbers are 41 , 43 , 127 , 99 , 71 , 92 , 71 , 58 , 57

Arranging the numbers in ascending order

41 , 43 , 57 , 58 , 71 , 71 , 92 , 99 , 127

n = 9 (odd)

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q6 . 25 , 34 , 31 , 23 , 22 , 26 , 35 , 29 , 20 , 32

SOLUTION :

Numbers are 25 , 34 , 31 , 23 , 22 , 26 , 35 , 29 , 20 , 32

Arranging the numbers in ascending order

20 , 22 , 23 , 25 , 26 , 29 , 31 , 32 , 34 , 35

n = 10(even)

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics
RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q7 . 12 , 17 , 3 , 14 , 5 , 8 , 7 , 15

SOLUTION :

Numbers are 12 , 17 , 3 , 14 , 5 , 8 , 7 , 15

Arranging the numbers in ascending order

3 , 5 , 7 , 8 , 12 , 14 , 15 , 17

n = 8(even)

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics
RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q8 . 92 , 35 , 67 , 85 , 72 , 81 , 56 , 51 , 42 , 69

SOLUTION :

Numbers are 92 , 35 , 67 , 85 , 72 , 81 , 56 , 51 , 42 , 69

Arranging the numbers in ascending order

35 , 42 , 51 , 56 , 67 , 69 , 72 , 81 , 85 , 92

n = 10(even)

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics
RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q9. Numbers 50 , 42 , 35 , 2x + 10 , 2x – 8 , 12 , 11 , 8 are written in descending order and their median is 25 , find x.

SOLUTION :

Given the number of observation , n = 8

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics
RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Given median = 25

∴ 2x+1 = 25

⇒ 2x = 24

⇒ x = 12

Q10 . Find the median of the following observations : 46 , 64 , 87 , 41 , 58 , 77 , 35 , 90 , 55 , 92 , 33 .If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?

SOLUTION :

Given the numbers are  46 , 64 , 87 , 41 , 58 , 77 , 35 , 90 , 55 , 92 , 33

Arranging the numbers in ascending order

33 , 35 , 41 , 46 , 55 , 58 , 64 , 77 , 87 , 90 , 92

n = 11 (odd)

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

If 92 is replaced by 99 and 41 by 43

Then the new values are : 33 , 35 , 43 , 46 , 55 , 58 , 64 , 77 , 87 , 90 , 99

n = 11 (odd)

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q11 . Find the median of the following data : 41 , 43 , 127 , 99 , 61 , 92 , 71 , 58 , 57 .If 58 is replaced by 85 , what will be the new median ?

SOLUTION :

Given the numbers are  41 , 43 , 127 , 99 , 61 , 92 , 71 , 58 , 57

Arranging the numbers in ascending order

41 , 43 , 57 , 58 , 61 , 71 , 92 , 99 , 127

n = 9 (odd)

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

If 58 is replaced by 85

Then the new values be in order are : 41 , 43 , 57, 61 , 71 , 85 , 92 , 99 , 127

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q12 . The weights (in kg) of 15 students are : 31 , 35 , 27 , 29 , 32 , 43 , 37 , 41 , 34 , 28 , 36 , 44 , 45 , 42 , 30.Find the median . If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg , find the new median .

SOLUTION :

Given the numbers are  31 , 35 , 27 , 29 , 32 , 43 , 37 , 41 , 34 , 28 , 36 , 44 , 45 , 42 , 30

Arranging the numbers in ascending order

27 , 28 , 29 , 30 , 31 , 32 , 34 , 35 , 36 , 37 , 41 , 42 , 43 , 44 , 45.

n = 15 (odd)

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q13. The following observation s have been arranged in ascending order. If the median of the data is 63 , find the value of x : 29 , 32 , 48 , 50 , x , x + 2 , 72 , 78 , 84 , 95.

SOLUTION :

Total number of observation in the given data is 10 (even number) . So median of this data will be mean of 10/2 i . e, 5th observation and  RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

So, median of data RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

The document RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
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FAQs on RD Sharma Solutions Ex-24.3, Measures Of Central Tendency, Class 9, Maths - RD Sharma Solutions for Class 9 Mathematics

1. What are measures of central tendency in statistics?
Ans. Measures of central tendency in statistics refer to the numerical values that represent the center or average of a set of data. They are used to provide a single value that represents the entire data set, making it easier to understand and analyze the data.
2. What are the different measures of central tendency?
Ans. There are three main measures of central tendency: mean, median, and mode. The mean is calculated by summing up all the values in the data set and dividing by the total number of values. The median is the middle value when the data set is arranged in ascending or descending order. The mode is the value that appears most frequently in the data set.
3. How is the mean calculated and what does it represent?
Ans. The mean is calculated by summing up all the values in the data set and dividing by the total number of values. It represents the average value of the data set. It is often used when the data is normally distributed and there are no extreme outliers.
4. When is the median a better measure of central tendency than the mean?
Ans. The median is a better measure of central tendency than the mean when there are extreme outliers in the data set. Outliers can significantly affect the value of the mean, making it not representative of the majority of the data. In such cases, the median, which is not affected by outliers, provides a more accurate representation of the center of the data.
5. How is the mode useful in data analysis?
Ans. The mode is useful in data analysis as it helps identify the most frequently occurring value in a data set. It is particularly useful when dealing with categorical or discrete data. The mode can provide insights into the characteristics or preferences of a population, and can be used to make decisions or predictions based on the most common value.
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