**Chapter – 5 Measures Of Central Tendency**

**I. Choose the correct answers (each question carries 1 mark). **

**1. Five students obtained 10, 20, 30, 40 and 50 marks respectively. What would be the mean? **

a) 35

b) 30

c) 25

d) 40

**2. X = xNΣis concerned with **

a) Arithmetic Mean

b) Mode

c) Median

d) Geometric Mean

**3. The most commonly used measure of central tendency is **

a) Mode

b) Median

c) Arithmetic mean

d) Percentile

**4. Which of the following represent Median? **

**5. Percentiles divide the distribution equal into **

a) 100 parts

b) 75 parts

c) 25parts

d) 50 parts

**6. Quartiles are measures which divide the data into **

a) 2 equal parts

b) 4 equal parts

c) 1 equal parts

d) 3 equal parts

**7. Assign weights to various item according to their importance is called **

a) Arithmetic a wean

b) median

c) weighted Arithmetic mean

d) mode

**8. What would be the median wage for the following wages of 5 labourers 10, 20, 30, 35, 38 **

a) Rs 20

b) Rs 10

c) Rs 35

d) Rs 30

**II. Fill in the blanks (each question carries 1 mark). **

1. ………………. Arithmetic mean gives relative importance to each item

2. 3rd quartile and ………………. percentile are the same.

3. There are ………………. Quartiles in a series.

4. ………………. is not affected by the extreme values.

5. Most frequently observed value in a series is called ……………….

6. A distribution with more than two modes is called ……………….

**III. Match the following: (total 5 marks). **

**IV. Answer the following questions in a word / sentence (each question carries 1 mark). **

1. What is meant by central tendency?

2. What is the meaning of Arithmetic mean?

3. Define median

4. Pocket money of 8 students is Rs 6, 12, 18, 24, 30, 36, 42, and 48 calculate arithmetic mean.

5. Write the formula for weighted mean.

6. What do you mean by percentiles?

7. What is Bi-model?

8. Calculate mode from the following data

X: 10, 8, 10, 6, 4, 12, 10, 8, 10, 18, 16, 10, 18, 16.

**V. Answer the following questions in about four sentences (each question carries 2 marks) **

1. What are the types of measures of central tendency?

2. Calculate arithmetic mean from the following data.

Marks obtained by 10 students 30, 62, 47, 25, 52, 39, 56, 66, 12, 24

3. Calculate the value of median from the following figures.

X: 5 7 9 12 11 8 7 15 25

4. How do you classify modal series.

5. What is mode? Give formula to find out mode in continuous series.

**VI. Answer the following questions in about twelve sentences (each question carries 4 marks) **

1. Calculate the arithmetic mean from the following data.

X | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 |

f | 5 | 7 | 9 | 10 | 8 | 6 | 5 | 2 |

2. Define weighted mean? How do you calculate it? Explain.

3. Name and define any three statistical average.

4. Calculate median from the following data.

Weight | 40 | 50 | 60 | 70 | 80 | 90 |

No of persons | 3 | 17 | 24 | 16 | 8 | 2 |

5. Calculate the lower quartile from the following data.

X: 22 26 14 30 18 11 35 41 12 32

**VII. Answer the following in about twenty sentences.** (Each question carries 6 marks)

1. Calculate arithmetic mean by direct, assumed mean and step deviation methods for the following data. 40, 50, 55, 78, 58

2. Calculate average marks of the following students using

a) Direct method b) step deviation method.

Marks (x) | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |

No of students (f) | 5 | 12 | 15 | 25 | 8 | 3 | 2 |

3. Find median of the following data.

Wages | 60-70 | 50-60 | 40-50 | 30-40 | 20-30 |

No of workers | 7 | 21 | 11 | 6 | 5 |

6. Find the mode of labour family from following data

Monthly income (*in 000) | Cumulative frequency |

Below 50 | 97 |

Below 45 | 95 |

Below 40 | 90 |

Below 35 | 80 |

Below 30 | 60 |

Below 25 | 30 |

Below 20 | 12 |

Below 15 | 4 |

**VIII. Project oriented question (5 marks) **

1. As per recorded temperature per two hours in a day from 6 am to 6 pm, calculate the range and mean temperature of a day.

Hour | Temperature |

6-8 | 18 |

8-10 | 24 |

10-12 | 26 |

12-14 | 29 |

14-16 | 30 |

16-18 | 25 |