# Best Suited Measure of Central Tendency in Different Cases and the Empirical Relationship between Them

## Trending Questions

**Q.**

Consider the following distribution of daily wages of 50 workers of a factory.

Daily wages (in Rs) |
500 − 520 |
520 − 540 |
540 − 560 |
560 − 580 |
580 − 600 |

Number of workers |
12 |
14 |
8 |
6 |
10 |

Find the mean daily wages of the workers of the factory by using an appropriate method.

**Q.**

Find the mean of the first five prime numbers?

**Q.**

The mean and mode of a frequency distribution are 28 and 16 respectively. The median is

(a) 22 (b) 23.5 (c) 24 (d) 24.5

**Q.**

A survey regarding the heights (in cm) of 50 girls of a class was conducted and the following data was obtained:

Height (in cm)120−130130−140140−150150−160160−170TotalNumber of girls281220850

Find the mean, median and mode of the above data.

**Q.**An incomplete frequency distribution is given below Median value is 46, the missing frequency is

Variate | Frequency |

10−20 | 12 |

20−30 | 30 |

30−40 | ? |

40−50 | 65 |

50−60 | 45 |

60−70 | 25 |

70−80 | 18 |

Total | 229 |

- 34
- 35
- 26
- 33

**Q.**

Find the mode, median and mean for the following data:Marks obtained25−3535−4545−5555−6565−7575−85Number ofstudents7313317111

**Q.**

Mean of first six prime numbers is

$4.83$

$6.83$

$5.83$

$7.83$

**Q.**

Find the mean, median and mode of the following data:

Class0−2020−4040−6060−8080−100100−120120−140Frequency681012653

**Q.**

Given below are the weekly wages of 200 workers in a small factory.

Calculate the maean weekly wages of the workers.

145

200

150

130

**Q.**

Assertion-and-Reason Type

Each question consists of two statements, namely, Assertion (A) and Reason (R).For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are the true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

Assertion (A)Reason (R)If the median and mode of a Mean, median and mode of afrequency distribution are 150 and frequency distribution are related as:154 respectively, then its mean is 148.mode=3 median−2 mean.

The correct answer is :(a)/(b)/(c)/(d).

**Q.**

If the mean and median of a set of numbers are 8.9 and 9 respectively then the mode will be

(a) 7.2 (b) 8.2 (c)9.2 (d)10.2

**Q.**

For a certain distribution, mode and median were found to be 1000 and 1250 repsectively.Find mean for this distribution using an empirical relation.

**Q.**

Which measure of central tendency will a shoe manufacturer make use of to determine the size(s) which he should manufacture in maximum quantity?

Mean

Median

Mode

Standard deviation

**Q.**Find mean, if median = 20.6 and mode = 26.

- 17.9
- 20
- 15
- 18.2

**Q.**

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.

**Q.**

Find the mean, median and mode of the following data:

Class0−5050−100100−150150−200200−250250−300300−350Frequency2356531

**Q.**

A maths aptitude test of 50 students was recorded as follows. Calculate the mode by drawing a histogram.

80

82

83

84

81

85

**Q.**

Given below are the weekly wages of 200 workers in a small factory:

Calculate the mean weekly wage of the workers.

145

143

150

146

147

**Q.**

Find the mean, mode and median of the following frequency distribution:

Class0−1010−2020−3030−4040−5050−6060−70Frequency510183020125

**Q.**

In a diagnostic test in mathematics given to students, the following marks (out of $100$) are recorded: $46,52,48,11,41,62,54,53,96,40,98,44$. Which ‘average’ will be a good representative of the above data and why?

**Q.**

The following are the marks obtained in Science by students in class X.

The mean of the given data is 63.33.

Is this mean an appropriate representation of the average marks obtained?

If no, what would be the most appropriate measure of central tendency for the correct representation of the marks distribution?

What is the value of this measure of central tendency for the given data?

MarksFrequency10−20120−30030−40040−50050−60160−70570−801580−902090−1003

No, median, value of median = 80.12

No, mode, value of mode = 85

Yes, the value of mean represents this data the best

Yes, mean is the best measure of an average

**Q.**Variance of certain number of scores is 16 and the mean is 10 then the coefficient of variation is?

**Q.**

Find the mean, median and mode of:

3, 0, 2, 2, 4, 3, 5, 4, 4, 3, 4

**Q.**

The following table gives the daily income of 50 workers of a factory:

Daily income(in Rs.)100−120120−140140−160160−180180−200Number of workers12148610

Find the mean, mode and median of the above data.

**Q.**

Find the mean deviation about mean for the following data

38, 70, 48, 40, 42, 55, 63, 46, 54, 44

**Q.**Find the mean and median for the following data:

i)13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

ii)36, 72, 46, 42, 60, 45, 53, 46, 51, 49

**Q.**

The relationship between Mean, Median and Mode is

Median = Mean + Mode

Mode = 3 median - 2 mean

Mode = 2 median - 3 mean

3Mode = 2 median - 3 mean

**Q.**The following table shows the daily wages of workers in a factory:

Daily wages (in Rs) | 0-100 | 100-200 | 200-300 | 300-400 | 400-500 |

Number of workers | 40 | 32 | 48 | 22 | 8 |

Find the median daily wage income of the workers.

**Q.**

Find the mean deviation about median for the following data

Marks0−1010−2020−3030−4040−5050−60No. of girls4891075

**Q.**

Which measure of center should you use to describe two data sets that are both symmetric?