RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math | RD Sharma Solutions for Class 7 Mathematics PDF Download

Question 1:

A die was thrown 20 times and the following scores were recorded:
 5, 2, 1, 3, 4, 4, 5, 6, 2, 2, 4, 5, 5, 6, 2, 2, 4, 5, 5, 1
 Prepare the frequency table of the scores on the upper face of the die and find the mean score.

Answer 1:

The frequency table for the given data is as follows:

In order to compute the arithmetic mean, we prepare the following table:

                                  Computation of Arithmetic Mean

Question 2:

The daily wages (in Rs) of 15 workers in a factory are given below:
 200, 180, 150, 150, 130, 180, 180, 200, 150, 130, 180, 180, 200, 150, 180
 Prepare the frequency table and find the mean wage.

Answer 2:

The frequency table for the given data is as follows:

In order to compute the mean wage, we prepare the following table:

Mean wages of the workers

xi	fi	fi xi
130	2	260
150	4	600
180	6	1080
200	3	600
Total

Question 3:

The following table shows the weights (in kg) of 15 workers in a factory:

Calculate the mean weight.

Answer 3:

                                    Calculation of Mean

Calculation of Mean

xi	fi	fi xi
60	4	240
63	5	315
66	3	198
72	1	72
75	2	150
Total

Question 4:

The ages (in years) of 50 students of a class in a school are given below:

Find the mean age

Answer 4:

        Calculation of Mean

xi	fi	fi xi
14	15	210
15	14	210
16	10	160
17	8	136
18	3	54
Total

Question 5:

Calculate the mean for the following distribution:

Answer 5:

                       Calculation of Mean

xi	fi	fi xi
5	4	20
6	8	48
7	14	98
8	11	88
9	3	27
Total

Question 6:

Find the mean of the following data:

Answer 6:

                    Calculation of Mean

xi	fi	fixi
19	13	247
21	15	315
23	16	368
25	18	450
27	16	432
29	15	435
31	13	403
Total

Question 7:

The mean of the following data is 20.6. Find the value of p.

Answer 7:

            Calculation of Mean

xi	fi	fi xi
10	3	30
15	10	150
p	25	25p
25	7	175
35	5	175
Total

We have: 

⇒20.6×50 = 530 +25p  ⇒1030 = 530 +25p
⇒1030 − 530 = 25p  ⇒500 = 25p
⇒p = 500/25 ⇒ p = 20

Question 8:

If the mean of the following data is 15, find p.

Answer 8:

                                 Calculation of Mean

xi	fi	fi xi
5	6	30
10	p	10p
15	6	90
20	10	200
25	5	125
Total

We have:

⇒15 (27 +p) = 445 +10p ⇒405 + 15p =445 +10p
⇒15p − 10p = 445 −405 ⇒5p = 40 ⇒p = 40÷5

Therefore, p =  8.

Question 9:

Find the value of p for the following distribution whose mean is 16.6

Answer 9:

                     Calculation of Mean

xi	fi	fixi
8	12	96
12	16	192
15	20	300
p	24	24p
20	16	320
25	8	200
30	4	120
Total

We have:

⇒16.6×100 = 1228 +24p
⇒1660 = 1228 +24p
⇒1660 − 1228 = 24p
⇒432 = 24p
⇒p = 432/24
⇒p =18

Question 10:

Find the missing value of p for the following distribution whose mean is 12.58

Answer 10:

                      Calculation of Mean

xi	fi	fixi
5	2	10
8	5	40
10	8	80
12	22	264
p	7	7p
20	4	80
25	2	50
Total

We have:

⇒12.58×50 = 524 +7p
⇒629 = 524 +7p
⇒629 − 524 = 7p
⇒105 = 7p
⇒p = 105/ 7
⇒p =15.

Question 11:

Find the missing frequency (p) for the following distribution whose mean is 7.68

Answer 11:

             Calculation of Mean

xi	fi	fi xi
3	6	18
5	8	40
7	15	105
9	p	9p
11	8	88
13	4	52
Total

We have:

⇒7.68 × (41 +p) =303 +9p
⇒314.88 + 7.68p = 303 +9p 
⇒314.88 −303 = 9p −7.68p
⇒11.88 = 1.32p

Question 12:

Find the value of p, if the mean of the following distribution is 20

Answer 12:

              Calculation of Mean

xi	fi	fi xi
15	2	30
17	3	51
19	4	76
20 + p	5p	(20+p)5p
23	6	138
Total

We have:

⇒20 × (15 +5p) =295 + (20+p)5p⇒300+ 100p = 295 +100p + 5p

⇒ 300 - 295 + 100p -100p = 5p² 
⇒ 5 = 5p² 
⇒ p² = 1