RD Sharma solution class 7 chapter 23 Data Handling II(Central values) Objective Type Questions

Objective Type Questions

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Question 1:

If the mean of observations 7, 8, 9, 11 and x is 10, then x =

(a) 10                                    (b) 15                                (c) 12                                 (d) 13

Answer 1:

Given : the mean of the observations 7, 8, 9, 11 and x is 10.
$$\begin{gathered} \mathrm{Mean} \mathrm{of} \mathrm{observations}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}} \\ \Rightarrow 10=\frac{7+8+9+11+x}{5} \\ \Rightarrow 35+x=50 \\ \Rightarrow x=50-35=15 \end{gathered}$$
Thus, the value of x is 15.
Hence, the correct option is (b).

Question 2:

If the mean of observations 20, 42, 35, 45 and x is 37, then x =

(a) 43                                    (b) 42                                (c) 44                                 (d) 45

Answer 2:

Given : the mean of the observations 20, 42, 35, 45 and x.
$$\begin{gathered} \mathrm{Mean} \mathrm{of} \mathrm{observations}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}} \\ \Rightarrow 37=\frac{20+42+35+45+x}{5} \\ \Rightarrow 142+x=185 \\ \Rightarrow x=185-142=43 \end{gathered}$$
Thus, the value of x is 43.
Hence, the correct option is (a).

Question 3:

The mean of first five natural numbers is

(a) 5                                    (b) 4                                (c) 3                                 (d) 6

Answer 3:

The first five natural numbers are: 1, 2, 3, 4, 5.
$$\begin{gathered} \mathrm{Mean}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}} \\ =\frac{1+2+3+4+5}{5} \\ =\frac{15}{5} \\ =3 \end{gathered}$$
Thus, the mean of first five natural number is 3.
Hence, the correct option is (c).

Question 4:

The mean of first five prime numbers is

(a) 5.6                                 (b) 5.5                               (c) 5.4                                 (d) 5.2

Answer 4:

The first five prime numbers are: 2, 3, 5, 7, 11.
$$\begin{gathered} \mathrm{Mean}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}} \\ =\frac{2+3+5+7+11}{5} \\ =\frac{28}{5} \\ =5.6 \end{gathered}$$
Thus, the mean of first five prime numbers is 5.6.
Hence, the correct option is (a).

Question 5:

The mean of first seven even natural numbers is

(a) 7                                 (b) 8                               (c) 9                                 (d) 6

Answer 5:

The first seven even natural numbers are: 2, 4, 6, 8, 10, 12, 14.
$$\begin{gathered} \mathrm{Mean}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}} \\ =\frac{2+4+6+8+10+12+14}{7} \\ =\frac{56}{7} \\ =8 \end{gathered}$$
Thus, the mean of first seven even natural numbers is 8.
Hence, the correct option is (b).

Question 6:

The mean of first six multiples of 5 is

(a) 3.5                                 (b) 18.5                               (c) 17.5                                 (d) 30

Answer 6:

The first six multiples of 5 are: 5, 10, 15, 20, 25, 30.
$$\begin{gathered} \mathrm{Mean}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}} \\ =\frac{5+10+15+20+25+30}{6} \\ =\frac{105}{6} \\ =17.5 \end{gathered}$$
Thus, the mean of first six multiples of 5 is 17.5.
Hence, the correct option is (c).

Question 7:

The mean of five numbers is 4. If 1 is added to each other, then the new mean is

(a) 4                                 (b) 5                               (c) 3                                 (d) 5.5

Answer 7:

Mean of five numbers = 4
Sum of five numbers = 5 $\text{×}$ 4 = 20
$$\begin{gathered} \mathrm{New} \mathrm{mean}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}} \\ =\frac{20+1+1+1+1+1}{5} \\ =\frac{25}{5} \\ =5 \end{gathered}$$
Thus, the new mean is 5.
Hence, the correct option is (b).

Question 8:

If the sum of 10 observations is 95, then their mean is

(a) 9.5                                 (b) 10                               (c) 950                                 (d) 95

Answer 8:

Sum of 10 observations = 95
$$\begin{gathered} \mathrm{Mean}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}} \\ =\frac{95}{10} \\ =9.5 \end{gathered}$$
Thus, the mean is 9.5.
Hence, the correct option is (a).

Question 9:

If the mean of n observations is 12 and the sum of the observations is 132, then the value of n is

(a) 9                                 (b) 10                               (c) 11                                 (d) 12

Answer 9:

Mean of n observations = 12
Sum of observations = 132
$$\begin{gathered} \mathrm{Mean}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}} \\ \Rightarrow 12=\frac{132}{n} \\ \Rightarrow n=\frac{132}{12}=11 \end{gathered}$$
Thus, the value of n is 11.
Hence, the correct option is (c).

Question 10:

The median of the data 9, 12, 11, 10, 8, 9, 11 is

(a) 10                                 (b) 11                               (c) 9                                 (d) None of these

Answer 10:

Arranging the given data in increasing order, we get
8, 9, 9, 10, 11, 11, 12
As the number of observations is odd (7), the median is the middle term which is 10.
Hence, the correct option is (a).

Question 11:

The median of the data 5, 7, 9, 10, 11 is

(a) 7                                 (b) 9                               (c) 11                                 (d) 10

Answer 11:

The data in arranging order is : 5, 7, 9, 10, 11
As the number of observations is odd (5), the median is the middle term which is 9.
Hence, the correct option is (b).

Question 12:

The mean of a data is 15 and the sum of the observations is 195. The number of observations is

(a) 13                                 (b) 19                               (c) 16                                 (d) 17

Answer 12:

Mean of data = 15
Sum of observations = 195
$$\begin{gathered} \mathrm{Mean}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}\left(n\right)} \\ \Rightarrow 15=\frac{195}{n} \\ \Rightarrow n=\frac{195}{15}=13 \end{gathered}$$
Thus, the number of observations is 13.
Hence, the correct option is (a).

Question 13:

The median of 11 observations is 10. The number of possible observations in the data which are less than 10 is

(a) 5                                 (b) 6                               (c) 3                                 (d) 10

Answer 13:

Median divides the data into two equal parts. Since, the number of observations is 11, so
after arranging in increasing or decreasing order, the number of observations to the left
of the median is five.
Thus, the required number of observations is 5.
Hence, the correct option is (a).

Question 14:

If the mode of 22, 21, 23, 24, 21, 20, 23, 26, x and 26 is 23, then x =

(a) 20                                 (b) 21                               (c) 23                                 (d) 24

Answer 14:

Arranging the numbers 22, 21, 23, 24, 21, 20, 23, 26 and 26 in increasing order, we get
20, 21, 21, 22, 23, 23, 24, 26, 26
Here, the frequencies 21, 23 and 24 is 2.
So, for 23 to be the mode of the data, the value of x should be 23.
Hence, the correct option is (c).

Question 15:

If the mean of 5, 7, x, 10, 5 and 7 is 7, then x =

(a) 6                                 (b) 7                               (c) 8                                 (d) 9

Answer 15:

Here, the observations are 5, 7, x, 10, 5 and 7.
$$\begin{gathered} \mathrm{Mean}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}} \\ \Rightarrow 7=\frac{5+7+x+10+5+7}{6} \\ \Rightarrow x+34=42 \\ \Rightarrow x=42-34=8 \end{gathered}$$
Hence, the correct option is (c).

Question 16:

The mean of p, q and r is same as the mean of q, 2r and s. Then which of the following is correct?

(a) p = q = r              (b) q = r = s                     (c) q = r                           (d) p = r + s
 

Answer 16:

Mean of p, q and r = Mean of q, 2r and s
$$\begin{gathered} \frac{p+q+r}{3}=\frac{q+2r+s}{3} \\ \Rightarrow p+q+r=q+2r+s \\ \Rightarrow p=r+s \end{gathered}$$
Hence, the correct option is (d).

Question 17:

The mean of 10, 15, 19, 30, 43, 69 and x is x. Then the median is

(a) 19                           (b) 43                                 (c) 30                                   (d) None of these

Answer 17:

The mean of 10, 15, 19, 30, 43, 69 and x is x.
$$\begin{gathered} \therefore \mathrm{Mean}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}} \\ \Rightarrow x=\frac{10+15+19+30+43+69+x}{7} \\ \Rightarrow x+186=7x \\ \Rightarrow x=\frac{186}{6}=31 \end{gathered}$$
Thus, the observations are 10, 15, 19, 30, 43, 69 and 31.
Arranging the numbers 10, 15, 19, 30, 43, 69 and 31 in increasing order, we get
10, 15, 19, 30, 31, 43, 69
Thus, the median is 30.
Hence, the correct option is (c).

Question 18:

If the mean of 9, 10, 15, x, 6, 8 and 12 is 11. The median of the observations is

(a) 4                           (b) 10                                 (c) 13                                   (d) 5

Answer 18:

The mean of 9, 10, 15, x, 6, 8 and 12 is 11.
$$\begin{gathered} \therefore \mathrm{Mean}=\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}} \\ \Rightarrow 11=\frac{9+10+15+x+6+8+12}{7} \\ \Rightarrow x+60=77 \\ \Rightarrow x=77-60=17 \end{gathered}$$
So, the observations are 9, 10, 15, 17, 6, 8 and 12.
Arranging the the observations in increasing order, we get
9, 10, 15, 17, 6, 8, 12        or           6, 8, 9, 10, 12, 15, 17
Thus, the median is 10.
Hence, the correct option is (b).

Question 19:

The mode of the unimodular data 7, 8, 9, 8, 9, 10, 9, 10, 11, 10, 11, 12 and x is 10.
The value of x is

(a) 10                           (b) 9                                 (c) 8                                   (d) 11

Answer 19:

Arranging the data in ascending order, we get
7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12
Here, 10 has the maximum frequency (4).
Hence, the correct option is (a).

Question 20:

The mean weight of 21 students is 21 kg. If a student weighing 21 kg is removed from the group,
then the mean of of the remaining students is

(a) 20 kg                       (b) 21 kg                         (c) 19 kg                         (d) 18 kg

Answer 20:

Mean weight = 21 kg
Number of students = 21
Sum of weights of 21 students = 21 $\text{×}$ 21 = 441
Sum of weights of 20 students left = 441 − 21 = 420
Mean of remaining students = $\frac{420}{20}=21 \mathrm{kg}$
Hence, the correct option is (b).

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Question 21:

There are 7 observations in the data and their mean is 11. If each observation is multiplied by
2, then the mean of new observations is

(a) 11                       (b) 13                         (c) 22                         (d) 55

Answer 21:

Mean = 11
Number of observations = 7
Sum of observations = 11 $\text{×}$ 7 = 77
Sum of new observations = 2 $\text{×}$ 77 = 154
Mean of new observations = $\frac{154}{7}=22$
Hence, the correct option is (c).

Question 22:

The mean of 10 observations is 15. If one observation 15 is added, then the new mean is

(a) 16                       (b) 11                         (c) 10                         (d) 15

Answer 22:

Sum of 10 observations = 10 $\text{×}$ 15 = 150
Sum of 11 observations = 150 + 15 = 165
Number observations = 11
Mean of 11 observations = $\frac{165}{11}=15$
Thus, the new mean is 15.
Hence, the correct option is (d).

Question 23:

If the median of 10, 12, x, 6, 18 is 10, then which of the following is correct?

(a) $6\le x\le 10$                    (b) x < 6                      (c) x > 18                     (d) Either (a) or (b)

Answer 23:

Arranging the numbers 10, 12, 6, 18 in ascending order, we get
6, 10, 12, 18
Thus, for 10 to be the median of the data, x < 6 or $6\le x\le 10$.
Hence, the correct option is (d).

Question 24:

The mode of the data 9, x, 6, 3, 4, 9, 8, 6, 4, 6 is 6. Which of the following cannot be the value of x

(a) 8                                      (b) 7                                         (c) 6                                        (d) 9

Answer 24:

Arranging the data 9, 6, 3, 4, 9, 8, 6, 4, 6 in ascending order, we get
3, 4, 4, 6, 6, 6, 8, 9, 9
Since the mode of the data is 6, so the value of x cannot be 4 or 9.
Hence, the correct option is (d).

Question 25:

Which of the following is correct?

(a) Mode = 2 Median − 3 Mean                                      (b) Mode = 3 Median − Mean
(c) Mode − Mean = 3(Median − Mean)                          (d) Mode − Median = Median − Mean

Answer 25:

The relation between Mean, Median and Mode is Mode − Mean = 3(Median − Mean).
Hence, the correct option is (d).