RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

RD Sharma Solutions for Class 7 Mathematics

Created by: Abhishek Kapoor

Class 7 : RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

The document RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev is a part of the Class 7 Course RD Sharma Solutions for Class 7 Mathematics.
All you need of Class 7 at this link: Class 7

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:

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

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

                                  Computation of Arithmetic Mean

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

 

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:

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

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

Mean wages of the workers
xi fi fi xi
1302 260
1504 600
18061080
2003 600
TotalRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRevRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

 

Question 3:

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

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

Calculate the mean weight.

Answer 3:

                                    Calculation of Mean

Calculation of Mean

 xififi xi
 60 4240
63 5315
66 3198
72 172
75 2150
TotalRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRevRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev 

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

 

Question 4:

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

Age (in years):1415161718
Numbers of students:15141083

Find the mean age

Answer 4:

 

        Calculation of Mean

 xififi xi
 14 15210
15 14210
16 10160
17 8136
18 354
TotalRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRevRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev 

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

 

Question 5:

Calculate the mean for the following distribution:

:56789
f :4814113

Answer 5:

 

                       Calculation of Mean

 xififi xi
 5 420
6 848
7 1498
8 1188
9 327
TotalRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRevRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev 

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

 

Question 6:

Find the mean of the following data:

x:19212325272931
f:13151618161513

Answer 6:

                    Calculation of Mean

xififixi
1913 247
2115315
2316368
2518450
2716432
2915435
3113403
Total  RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRevRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

  RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

Question 7:

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

x:1015p2535
f:3102575

Answer 7:

            Calculation of Mean

xififi xi
10330
1510150
p2525p
257175
355175
TotalRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRevRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev


We have: 

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

⇒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.

x:510152025
f:6p6105

Answer 8:

                                 Calculation of Mean

xififi xi
5630
10p10p
15690
2010200
255125
TotalRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRevRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

We have:

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

⇒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

x:81215p202530
f:121620241684

Answer 9:

                     Calculation of Mean

xififixi
81296
1216192
1520300
p2424p
2016320
258200
304120
Total RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRevRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev


We have:

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

 

⇒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

x:581012p2025
f:25822742

Answer 10:

                      Calculation of Mean

xififixi
5210
8540
10880
1222264
p77p
20480
25250
Total RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRevRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev


We have:

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

⇒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

x:35791113
f:6815p84

Answer 11:

             Calculation of Mean

xififi xi
3618
5840
715105
9p9p
11888
13452
TotalRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRevRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev


We have:

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev
⇒7.68 × (41 +p) =303 +9p
⇒314.88 + 7.68p = 303 +9p 
⇒314.88 −303 = 9p −7.68p
⇒11.88 = 1.32p
RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

 

Question 12:

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

x:15171920 + p23
f:234p6

Answer 12:

              Calculation of Mean

xififi xi
15230
17351
19476
20 + p5p(20+p)5p
236138
TotalRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRevRD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev


We have:

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

RD Sharma Solutions (Part - 1) - Ex-23.2, Data Handling II Central Values, Class 7, Math Class 7 Notes | EduRev

 

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

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

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