# What are some important questions on Measures of Central Tendency?

In this post we will learn; What are some important questions on Measures of Central Tendency?

## Q1. If in an asymmetrical distribution median is 28 and mean is 31. What will be the value of mode?

Solution:

Mode = 3 Median – 2 Mean

Mode = (3 x 28) – (2 x 31) = 84 – 62

Mode = 22

## Q2. The mean of 10 items was 70. Later on it was found out that one item 92 was misread as 29. What was the correct mean?

Solution:

N = 10

Mean = 70

Mean = Summation of X / N

70 = Summation of X / 10

Summation of X = 70 x 10 = 700 (Wrong Sum)

Correct Sum = 700 – 29 + 92 = 763

Correct Mean = 763/10 = 76.3

## Q3. Average marks of 26 students of Section A of class XI is 73 and average marks of 24 students of Section B of class XI is 86. Find out the average marks of class XI.

Solution: Average Marks of A = 73

N1 = 26

Average Marks of B = 86

N2 = 24

Combined Mean = N1 (Mean of A) + N2 (Mean of B) / (n1+n2)

Combined Mean or Average Marks of Class XI = (26 x 73) + (24 x 86) / 50

Combined Mean = 1898 + 2064 / 50 = 3962/50

Average Marks of XI = 79.24

## Q4. Calculate arithmetic mean from the following data: (Using assume mean method)

X | Less than 10 | Less than 20 | Less than 30 | Less than 40 | Less than 50 |

f | 5 | 15 | 55 | 75 | 100 |

Solution: Arithmetic mean is 30.

## Q5. Calculate mode of the following series: (4)

Class | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 | 60-69 | 70-79 |

Frequency | 10 | 12 | 18 | 30 | 16 | 6 | 8 |

Solution:

## Q6. Calculate median from the following data: (4)

Marks | More than 0 | More than 10 | More than 20 | More than 30 | More than 40 | More than 50 |

No of Students | 50 | 42 | 38 | 28 | 16 | 3 |

Solution:

## Q7. The following series to the daily income of workers employed in a firm. Compute(a) highest income of lowest 50% workers (b) minimum income earned by the top 25% workers and (c) maximum income earned by lowest 25% workers.(6)

Daily Income | 10-14 | 15-19 | 20-24 | 25-29 | 30-34 | 35-39 |

Number of Workers | 5 | 10 | 15 | 20 | 10 | 5 |

Solution:

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I hope it was easy to digest. Take a look at the virtual explanation on my YouTube Channel:

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I hope it was helpful, you can refer to more posts related to the statistics.

- Individual Series Arithmetic Mean
- Discrete Series Arithmetic Mean
- Introduction to the statistics.
- Functions and importance of statistics.

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