# RD SHARMA Solutions for Class 9 Maths Chapter 24 - Measures of Central Tendency

## Chapter 24 - Measures of Central Tendency Exercise Ex. 24.1

The numbers of children in 10 families of a locality are:

2, 4, 3, 4, 2, 0, 3, 5, 1, 1, 5. Find the mean number of children per family.

**The traffic police recorded the speed (in km/hr) of 10 motorists as 47, 53, 49, 60, 39, 42, 55, 57, 52, 48. Later on an error in recording instrument was found. Find the correct average speed of the motorists if the instrument recorded 5 km/hr less in each case.**

If M is the mean of x_{1}, x_{2}, x_{3}, x_{4}, x_{5} and x_{6} , prove that

(x_{1} - M) + (x_{2} - M) + (x_{3} -M) + (x_{4} - M) + (x_{5 }- M) + (x_{6} - M) = 0

**(i)**

**(ii)**

## Chapter 24 - Measures of Central Tendency Exercise Ex. 24.2

**Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss. **

No. of heads per toss |
No. of tosses |

012345 |
3814434228716425 |

Total |
1000 |

x |
f |
xf |

10 | 17 | 170 |

30 | f_{1} |
30f_{1} |

50 | 32 | 1600 |

70 | f_{2} |
70f_{2} |

90 | 19 | 1710 |

N = 120 |

## Chapter 24 - Measures of Central Tendency Exercise Ex. 24.3

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

**The following observations 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**

## Chapter 24 - Measures of Central Tendency Exercise Ex. 24.4

**Find the mode of**

**14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18**

**Arranging the data in an ascending order**

**14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28**

**Here observation 14 is having the highest frequency i.e. 4 in given data. So, mode of given data is 14.**

**The demand of different sizes, as obtained by a survey, is given below:**

Size |
38 |
39 |
40 |
41 |
42 |
43 |
44 |
Total |

Number of persons (wearing it): |
26 |
39 |
20 |
15 |
13 |
7 |
5 |
125 |

**Find the modal shirt size, as observed from the survey.**

## Chapter 24 - Measures of Central Tendency Exercise 24.21

Which one of the following is not a measure of central value?

(a) Mean

(b) Range

(c) Median

(d) Mode

Range is not a measure of central value.

The difference between the highest value and the lowest value in the data set is called Range.

Hence, correct option is (b).

## Chapter 24 - Measures of Central Tendency Exercise 24.22

The mean of a set of seven numbers is 81. If one of the numbers is discarded, the mean of the remaining numbers is 78. The value of discarded number is

(a) 98

(b) 99

(c) 100

(d) 101

For which set of numbers do the mean, median and mode all have the same value?

(a) 2, 2, 2, 2, 4

(b) 1, 3, 3, 3, 5

(c) 1, 1, 2, 5, 6

(d) 1, 1, 1, 2, 5

Mean | Median | Mode | |

2, 2, 2, 2, 4 | 12/5 = 2.4 | 2 | 2 |

1, 3, 3, 3, 5 | 15/5 = 3 | 3 | 3 |

1, 1, 2, 5, 6 | 15/5 = 3 | 2 | 1 |

1, 1, 1, 2, 5 | 10/5 = 2 | 1 | 1 |

From above table, data 1, 3, 3, 3, 5 has mean, median, mode all have same value, i.e. 3.

Hence, correct option is (b).

For the set of numbers 2, 2, 4, 5 and 12, which of the following statements is true?

(a) Mean = Median

(b) Mean > Mode

(c) Mean < Mode

(d) Mode = Median

If the arithmetic mean of 7, 5, 13, x and 9 is 10, then the value of x is

(a) 10

(b) 12

(c) 14

(d) 16

If the mean of five observations x, x + 2, x + 4, x + 6, x + 8, is 11, then the mean of first three observations is

(a) 9

(b) 11

(c) 13

(d) none of these

Mode is

(a) least frequent value

(b) middle most value

(c) most frequent value

(d) none of these

Most Frequent value is called mode.

Hence, correct option is (c).

The following is the data of wages per day: 5, 4, 7, 5, 8, 8, 8, 5, 7, 9, 5, 7, 9, 10, 8

The mode of the data is

(a) 7

(b) 5

(c) 8

(d) 10

The median of the following data: 0, 2, 2, 2, -3, 5, -1, 5, 5, -3, 6, 6, 5, 6 is

(a) 0

(b) -1.5

(c) 2

(d) 3.5

The algebraic sum of the deviations of a set of n values from their mean is

(a) 0

(b) n - 1

(c) n

(d) n + 1

A, B, C are three sets of values of x:

A: 2, 3, 7, 1, 3, 2, 3

B: 7, 5, 9, 12, 5, 3, 8

C: 4, 4, 11, 7, 2, 3, 4

Which one of the following statements is correct?

(a) Mean of A = Mode of C

(b) Mean of C = Median of B

(c) Median of B = Mode of A

(d) Mean, Median and Mode of A are equal.

The empirical relation between mean, mode and median is

(a) Mode = 3 Median - 2 Mean

(b) Mode = 2 Median - 3 Mean

(c) Median = 3 Mode - 2 Mean

(d) Mean = 3 Median - 2 Mode

The empirical Relation between mean, median and mode is

Mode = 3 Median - 2 mean

Hence, correct option is (a).

The mean of a, b, c, d and e is 28. If the mean of a, c, and e is 24, what is the mean of b and d?

(a) 31

(b) 32

(c) 33

(d) 34

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