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**Question 1. The following number of goals were scored by a team in a series of 10 matches: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3 Find the mean, median and mode of these scores. Solution: **To find mean: Here, n = 10,

∴

= (28/10) = 2.8

∴ Mean = 2.8

To find median:

Arranging the given data in an ascending order, we have: 0, 1, 2, 3, 3, 3, 3, 4, 4, 5

For even observation, we have median

Thus, the median of the data = 3

To find the mode:

∵ In the given data 0 occurs 1 time, 1 occurs 1 time, 2 occurs 1 time, 3 occurs 4 times, 4 occurs 2 times, 5 occurs 1 time

∵ 3 occurs maximum number of times.

∴ Mode = 3.

**Question 2. In a Mathematics test given to 15 students, the following marks (out of 100) are recorded: 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60 Find the mean, median and mode of this data. Solution: **To find the mean:

=(822/15) = 54.8

Thus, mean = 54.8

To find median:

Arranging the given data in an ascending order, we have:

39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

∵ n = 15, an odd number

∴

= (16/2)^{th} term = 8^{th} term = 52

Thus, the median = 52

To find mode:

∵ In the given data, the observation 52 occurs 3 times, i.e., the maximum number of times.

∴ Mode = 52

**Question 3. 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 Solution: **Here, the given observations are in an ascending order.

∵ n = 10 (an even number of observations)

∴

Since, median = 63 [Given]

∴ x + 1 = 63**⇒ ** x = 63 – 1 = 62

Thus, the required value of x is 62.

**Question 4. Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18. Solution:** Arranging the given data in an ascending order: 14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28.

∴ The observation 14 is occurring the maximum number of times (i.e., 4 times)

∴ Mode of the given data = 14

**Question 5. Find the mean salary of 60 workers of factory from the following table:**

Salary in ₹ | Number of workers |

3000 | 16 |

4000 | 12 |

5000 | 10 |

6000 | 8 |

7000 | 6 |

8000 | 4 |

9000 | 3 |

10000 | 1 |

Total | 60 |

**Solution:** Let salaries be represented by x_{i} and number of corresponding workers by f_{i}.**Note: **The mean x of n observations having values as x_{1}, x_{2}, x_{3}, …, x_{n }and occurring with frequencies f_{1}, f_{2}, f_{3}, …, f_{n} respectively is given by

Here,

f_{1 }x x_{1} = 16 x 3000 = 48,000

f_{2} x x_{2} = 12 x 4000 = 48,000

f_{3} x x_{3} = 10 x 5000 = 50,000

f_{4 }x x_{4} = 8 x 6000 = 48,000

f_{5} x x_{5} = 6 x 7000 = 42,000

f_{6} x x_{6 }= 4 x 8000 = 32,000

f_{7} x x_{7 }= 3 x 9000 = 27,000

f_{8} x x_{8} = 1 x 10000 = 10,000

∴ = [48000 + 48000 + 50000 + 48000 + 42000 + 32000 + 27000 + 10000]

= 305000

and = 16 + 12 + 10 + 8 + 6 + 4 + 3 + 1 = 60

⇒

Thus, the mean salary = ₹ 5080.33

salary in ₹ (x_{i)} | number of workers (f_{i}) | (f_{i} x_{i}) |

3000 | 16 | 16 x 3000 = 48000 |

4000 | 12 | 12 x 4000 = 48000 |

5000 | 10 | 10 x 5000 = 50000 |

6000 | 8 | 8 x 6000 = 48000 |

7000 | 6 | 6 x 7000 = 42000 |

8000 | 4 | 4 x 8000 = 32000 |

9000 | 3 | 3 x 9000 = 27000 |

10000 | 1 | 1 x 10000 = 10000 |

Total |

Thus, the required mean salary = ₹ 5080.33

**Question 6. Give one example of a situation in which (i) The mean is an appropriate measure of central tendency. (ii) The mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.**

(ii) Median is a qualitative central tendency of a data.

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