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.

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**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.**

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**

**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.**

The frequency table for the given data is as follows:

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

x_{i} | f_{i} | f_{i}_{ }x_{i} |

130 | 2 | 260 |

150 | 4 | 600 |

180 | 6 | 1080 |

200 | 3 | 600 |

Total |

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

Calculate the mean weight.

Calculation of Mean

Calculation of Mean

x_{i} | f_{i} | f_{i} x_{i} |

60 | 4 | 240 |

63 | 5 | 315 |

66 | 3 | 198 |

72 | 1 | 72 |

75 | 2 | 150 |

Total |

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

Age (in years): | 14 | 15 | 16 | 17 | 18 |

Numbers of students: | 15 | 14 | 10 | 8 | 3 |

**Find the mean age**

**Answer 4:**

Calculation of Mean

x_{i} | f_{i} | f_{i} x_{i} |

14 | 15 | 210 |

15 | 14 | 210 |

16 | 10 | 160 |

17 | 8 | 136 |

18 | 3 | 54 |

Total |

**Calculate the mean for the following distribution:**

x : | 5 | 6 | 7 | 8 | 9 |

f : | 4 | 8 | 14 | 11 | 3 |

** Calculation of Mean**

x_{i} | f_{i} | f_{i} x_{i} |

5 | 4 | 20 |

6 | 8 | 48 |

7 | 14 | 98 |

8 | 11 | 88 |

9 | 3 | 27 |

Total |

**Find the mean of the following data:**

x: | 19 | 21 | 23 | 25 | 27 | 29 | 31 |

f: | 13 | 15 | 16 | 18 | 16 | 15 | 13 |

** Calculation of Mean**

x_{i} | f_{i} | f_{i}x_{i} |

19 | 13 | 247 |

21 | 15 | 315 |

23 | 16 | 368 |

25 | 18 | 450 |

27 | 16 | 432 |

29 | 15 | 435 |

31 | 13 | 403 |

Total |

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

x: | 10 | 15 | p | 25 | 35 |

f: | 3 | 10 | 25 | 7 | 5 |

Calculation of Mean

x_{i} | f_{i} | f_{i}_{ }x_{i} |

10 | 3 | 30 |

15 | 10 | 150 |

p | 25 | 25p |

25 | 7 | 175 |

35 | 5 | 175 |

Total |

We have:

â‡’20.6Ã—50 = 530 +25p â‡’1030 = 530 +25p

â‡’1030 âˆ’ 530 = 25p â‡’500 = 25p

â‡’p = 500/25 â‡’ p = 20

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

x: | 5 | 10 | 15 | 20 | 25 |

f: | 6 | p | 6 | 10 | 5 |

Calculation of Mean

x_{i} | f_{i} | f_{i}_{ }x_{i} |

5 | 6 | 30 |

10 | p | 10p |

15 | 6 | 90 |

20 | 10 | 200 |

25 | 5 | 125 |

Total |

We have:

â‡’15 (27 +p) = 445 +10p â‡’405 + 15p =445 +10p

â‡’15p âˆ’ 10p = 445 âˆ’405 â‡’5p = 40 â‡’p = 40Ã·5

Therefore*, p* = 8.

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

x: | 8 | 12 | 15 | p | 20 | 25 | 30 |

f: | 12 | 16 | 20 | 24 | 16 | 8 | 4 |

Calculation of Mean

x_{i} | f_{i} | f_{i}x_{i} |

8 | 12 | 96 |

12 | 16 | 192 |

15 | 20 | 300 |

p | 24 | 24p |

20 | 16 | 320 |

25 | 8 | 200 |

30 | 4 | 120 |

Total |

We have:

â‡’16.6Ã—100 = 1228 +24p

â‡’1660 = 1228 +24p

â‡’1660 âˆ’ 1228 = 24p

â‡’432 = 24p

â‡’p = 432/24

â‡’p =18

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

x: | 5 | 8 | 10 | 12 | p | 20 | 25 |

f: | 2 | 5 | 8 | 22 | 7 | 4 | 2 |

** Calculation of Mean**

x_{i} | f_{i} | f_{i}x_{i} |

5 | 2 | 10 |

8 | 5 | 40 |

10 | 8 | 80 |

12 | 22 | 264 |

p | 7 | 7p |

20 | 4 | 80 |

25 | 2 | 50 |

Total |

We have:

â‡’12.58Ã—50 = 524 +7p

â‡’629 = 524 +7p

â‡’629 âˆ’ 524 = 7p

â‡’105 = 7p

â‡’p = 105/ 7

â‡’p =15.

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

x: | 3 | 5 | 7 | 9 | 11 | 13 |

f: | 6 | 8 | 15 | p | 8 | 4 |

** Calculation of Mean**

x_{i} | f_{i} | f_{i}_{ }x_{i} |

3 | 6 | 18 |

5 | 8 | 40 |

7 | 15 | 105 |

9 | p | 9p |

11 | 8 | 88 |

13 | 4 | 52 |

Total |

We have:

â‡’7.68 Ã— (41 +p) =303 +9p

â‡’314.88 + 7.68p = 303 +9p

â‡’314.88 âˆ’303 = 9p âˆ’7.68p

â‡’11.88 = 1.32p

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

x: | 15 | 17 | 19 | 20 + p | 23 |

f: | 2 | 3 | 4 | 5 p | 6 |

** Calculation of Mean**

x_{i} | f_{i} | f_{i}_{ }x_{i} |

15 | 2 | 30 |

17 | 3 | 51 |

19 | 4 | 76 |

20 + p | 5p | (20+p)5p |

23 | 6 | 138 |

Total |

We have:

â‡’20 Ã— (15 +5p) =295 + (20+p)5pâ‡’300+ 100p = 295 +100p + 5p

â‡’ 300 - 295 + 100p -100p = 5p^{2}

â‡’ 5 = 5p^{2}

â‡’ p^{2}^{ }= 1