# Assumed Mean Method of Finding Mean

## Trending Questions

**Q.**Express each number as a product of its prime factors:

**Q.**

Find the mean of the following data, using assumed-mean method:

Class0−2020−4040−6060−8080−100100−120Frequency203552443831

**Q.**If the mean of the following frequency distribution is 18 , find the missing frequency .

Class interval : 11-13 13-15 15-17 17-19 19-21 21-23 23-25

Frequency: 3 6 9 13 f 5 4

**Q.**For what value of k will the consecutive terms 2K+1, 3K+3 and 5k-1 form an A. P?

**Q.**

Question 3

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

Expenditure (in Rs)Number of families1000−1500241500−2000402000−2500332500−3000283000−3500303500−4000224000−4500164500−50007

**Q.**

Question 4

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Number of students per teacherNumber of states/U.T15−20320−25825−30930−351035−40340−45045−50050−552

**Q.**

Find the mean marks per student, using assumed-mean method:

Marks0−1010−2020−3030−4040−5050−60Number of students12182720176

**Q.**

Find the class marks of classes $10-25$ and $35-55$

**Q.**

The following table gives the lifetime in days of 100 electricity tubes of a certain make:

Find the mean lifetime of electricity tubes by the step deviation method.

145

100

60

175

**Q.**

The mean of five numbers is 28. If one of the numbers is excluded, the mean gets reduced by 2. Find the excluded number.

36

34

22

33

**Q.**Question 1

Find the mean marks of students for the following distribution

MarksNumber of students0 and above 8010 and above 7720 and above 7230 and above 6540 and above 5550 and above 4360 and above 2870 and above 1680 and above 1090 and above 8100 and above 0

**Q.**The arithmetic mean of the following data is 25, find the value of k.

x_{i}: |
5 | 15 | 25 | 35 | 45 |

f_{i}: |
3 | k | 3 | 6 | 2 |

**Q.**Question 5

The daily income of a sample of 50 employee are tabulated as follows.

Income(in~Rs) 1−200201−400401−600601−800Number of employees1415147

Find the mean daily income of employees.

**Q.**

To find out the concentration of $S{O}_{2}$ in the air (in parts per million, i.e., ppm) , the data was collected for $30$ localities in a certain city and is presented below. Find the mean concentration of $S{O}_{2}$ in the air.

Concentration of SO_{2} ( in ppm) | Frequency |

0.00 – 0.04 | 4 |

0.04 – 0.08 | 9 |

0.08 – 0.12 | 9 |

0.12 – 0.16 | 2 |

0.16 – 0.20 | 4 |

0.20 – 0.24 | 2 |

**Q.**

The table below shows the daily expenditure on food of 30 households in a locality:

Daily expenditure (in Rs.)Number of households100−1506150−2007200−25012250−3003300−3502

Find:

(a) mean of daily expenditure on food.

(b) median of daily expenditure on food.

**Q.**

What is the symbol for the sample standard deviation?

**Q.**

Find the mean of the following data, using assumed-mean method:

Marks100−120120−140140−160160−180180−200Number of students102030155

**Q.**

Question 3

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency f.

Daily pocket allowance (in Rs)11−1313−1515−1717−1919−2121−2323−25Number of workers76913f54

**Q.**

The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city.

ExpenditureFrequencyExpenditureFrequency(in rupees)(xi)(fi)(in rupees)(xi)(fi)100−15024300−35030150−20040350−40022200−25033400−45016250−30028450−5007

Find the average expenditure (in rupees) per household.

**Q.**If the mean of the following distribution is 2.6, then the value of y is

Variable (x): | 1 | 2 | 3 | 4 | 5 |

Frequency | 4 | 5 | y | 1 | 2 |

(a) 3

(b) 8

(c) 13

(d) 24

**Q.**

Calculate the mean of the following distribution:

Class IntervalFrequency0−10810−20520−301230−403540−502450−6016

**Q.**

Find the harmonic mean of the given numbers

12, 14, 16

3611

14

2136

41

**Q.**

Mean of $6$ observations is $10$ and their variance is $\frac{20}{3}$. If their observations are $15,11,10,7,a,b$ then $\left|a-b\right|$ is equal to:

$2$

$1$

$3$

$4$

**Q.**

Find the value of $f$ if the mean of the following distribution is $25.2$.

Class-interval | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ |

Frequency | $8$ | $12$ | $f$ | $11$ | $9$ |

**Q.**

While calculating the mean of a given data by the assumed-mean method, the following values were obtained:

A=25, ∑fidi=110, ∑fi=50.

Find the mean.

**Q.**

Calculate the mean of the distribution given below using the short cut method

Marks11−2021−3031−4041−5051−6061−7071−80No. of students261012974

**Q.**For the month of February, a class teacher of Class IX has the following absentee record for 45 students. Find the mean number of days, a student was absent.

Number of days of absent0−44−88−1212−1616−2020−24Number of students1836201

**Q.**

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method.

Literacy rate (in %)No. of cities45−55355−651065−751175−85885−953

66.44

69.43

67.39

71.55

**Q.**

A student scores $56$ on a geography test and $246$ on a mathematics test. The geography test has a mean of $80$ and a standard deviation of $20$. The mathematics test has a mean of $300$ and a standard deviation of $36$. If the data for both tests are normally distributed, on which test did the student score better?

**Q.**

Consider the following distribution of the number of mangoes being packed in cardboard boxes where these boxes contain varying number of mangoes. Find the mean number of mangoes kept in a packing box using assumed mean method.

Number of Mangoes50−5253−5556−5859−6162−64Number of boxes1511013511525

Can the assumed mean be 60?

- 53.87, yes
- 59.95, no
- 57.18, yes
- 54.99, no