# Weighted Mean Formula Used In Thesis Statements

**Weighted Mean** is a measurement of central tendency. It represents the average of a given data. Weighted mean is similar to arithmetic mean or sample mean. Weighted mean is calculated when data is given in a different way compared to an arithmetic mean or sample mean.

Sometimes, there are frequencies assigned to each term in the given data, then we can no longer use simple arithmetic mean formula. Few values may occur more frequently than others, therefore corresponding frequencies are allotted to each value. These frequencies are often referred as weights . In this case, weighted mean formula is used.

Weighted mean formula is as follows:

Where, $\bar{x}$ = weighted mean.

x_{i} = x_{1,}x_{2},x_{3......} = Items given.

and f_{i }= f_{1},f_{2},f_{3},...... = Frequencies corresponding to the given items.

## Weighted Mean Problems

Back to TopFew problems based on weighted mean formula are given below:

### Solved Examples

**Question 1:**The marks obtained by 20 students in a mathematics test are 12, 15, 18, 10, 20 and the corresponding frequencies are 3, 6, 5, 4, 2. Compute the average marks obtained by the students ?

**Solution:**

**Compute the following table using the information given the question**

x_{i } | f_{i } | f_{i}x_{i } |

12 | 3 | 36 |

15 | 6 | 90 |

18 | 5 | 90 |

10 | 4 | 40 |

20 | 2 | 40 |

$\sum f_{i}$ = 20 | $\sum f_{i}x_{i}$ = 296 |

Formula for weighted mean

$\bar{x}$ = $\frac{\sum f_{i}x_{i}}{\sum f_{i}}$

Substitute the subsequent values

$\bar{x}$ = $\frac{296}{20}$

= 14.8

**Question 2:**The number of students absent in a class on few subsequent days are as follows: 1, 3, 4, 4, 1, 7, 5, 2, 4, 3, 7, 3, 4, 5, 3, 5, 7, 7. Find the average number of absent students using weighted mean formula ?

**Solution:**

Write the frequency of each individual term:

x_{ i } | f_{ i } |

1 | 2 |

2 | 1 |

3 | 4 |

4 | 4 |

5 | 3 |

7 | 4 |

Construct the following table:

x_{i } | f_{i } | f_{i}x_{i } |

1 | 2 | 2 |

2 | 1 | 2 |

3 | 4 | 12 |

4 | 4 | 16 |

5 | 3 | 15 |

7 | 4 | 28 |

$\sum f_{i}$ = 18 | $\sum f_{i}x_{i}$ = 75 |

Write the formula for weighted mean.

$\bar{x}$ = $\frac{\sum f_{i}x_{i}}{\sum f_{i}}$

Substitute the values from table:

$\bar{x}$ = $\frac{75}{18}$ = 4.1

Since there are number of students which can not be in decimal, hence round it to the nearest integer.

4.1 = 4 students (approx.)

People who have acquired a disease, especially a life-threatening disease, arerushed to the hospital for treatment. “They seek help from professional health careworkers (HCWs) to alleviate the pain, signs, and symptoms, and eventually the diseaseitself. Health care workers are those clinical and other staff, including those in primarycare, who have regular, clinical contact with patients. This includes staff such as doctors,dentists and nurses, paramedical professionals such as occupational therapists,physiotherapists, radiographers, ambulance workers and porters, and students in thesedisciplines (The Association of National Health Occupational Physicians or ANHOPS).”These health care workers are the front liners in giving medical treatment andcare to the patients (A person under health care. The person may be waiting for thiscare, may be receiving it, or may have already received it). Because of this, “the healthof the HCWs is compromised or at risk all the time for

a vast array of infections thatcause substantial illness and

occasional deaths.” Despite this, few studies haveexamined the

incidence, prevalence, or exposure-associated rates of infection

or haveconsidered infection-specific interventions recommended in

maintaining work safety.(Sepkowitz,1996).“More than 10 years have elapsed since the last major consideration of occupationally acquired infections in health care workers. Since then, much haschanged—new infections have been identified, diagnostic tests for previously recognizeddiseases have been improved, the use of molecular epidemiologic techniques inoutbreak investigations has increasingly become routine, and outpatient and home carehave become more common.”(Sepkowitz, 1996)

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