Question

Madhu worked $ 2\dfrac{1}{2} $ hours on Monday, $ 3\dfrac{1}{4} $ hours on Tuesday, and $ 2\dfrac{3}{4} $ hours on Wednesday. What is the mean number of hours she worked on these three days?

Answer 1

Hint: The mean of a given set of data is generally the average of those numbers. Average of $ n $ data is the ratio between the sum of all the data and the total number of data $ n $ . Using these we will calculate the mean of the given data which will be our required answer.
Formula used:
If $ {a_1},{a_2},...,{a_n} $ represents $ n $ data then the average of the data is given by the formula
 $ \bar x = \dfrac{{{a_1} + {a_2} + ... + {a_n}}}{n} $

Complete step-by-step answer:
According to the question given to us
Madhu worked $ 2\dfrac{1}{2} $ hours on Monday,
Let $ {x_1} = 2\dfrac{1}{2} $
Madhu worked $ 3\dfrac{1}{4} $ hours on Tuesday,
Let $ {x_2} = 3\dfrac{1}{4} $
Madhu worked $ 2\dfrac{3}{4} $ hours on Wednesday
Let $ {x_3} = 2\dfrac{3}{4} $
Now we have the following data $ {x_1} = 2\dfrac{1}{2} $ , $ {x_2} = 3\dfrac{1}{4} $ , $ {x_3} = 2\dfrac{3}{4} $
Converting these mixed fractions to proper fractions we get:
 $ {x_1} = \dfrac{5}{2} $ , $ {x_2} = \dfrac{{13}}{4} $ , $ {x_3} = \dfrac{{11}}{4} $
Now by converting these to their decimal expression we get:
 $ {x_1} = 2.5 $ , $ {x_2} = 3.25 $ , $ {x_3} = 2.75 $
Clearly, there are three numbers so the mean is,
 $ \bar x = \dfrac{{{x_1} + {x_2} + {x_3}}}{3} $
 $ \Rightarrow \bar x = \dfrac{{2.5 + 3.25 + 2.75}}{3} $
 $ \Rightarrow \bar x = \dfrac{{8.5}}{3} $
Converting this to fraction we get:
 $ \bar x = \dfrac{{85}}{{30}} = \dfrac{{17}}{6} $
Converting into mixed fraction we get:
 $ \bar x = 2\dfrac{5}{6} $
Therefore, the mean is $ \bar x = 2\dfrac{5}{6} $
So, if Madhu worked $ 2\dfrac{1}{2} $ hours on Monday, $ 3\dfrac{1}{4} $ hours on Tuesday, and $ 2\dfrac{3}{4} $ hours on Wednesday, then the mean numbers of hour she worked is $ \bar x = 2\dfrac{5}{6} $ hours.
So, the correct answer is “$ \bar x = 2\dfrac{5}{6} $ hours”.

Note: Always convert the given data into the decimal expression and calculate the answer after doing this convert it to the actual form as it was given earlier. By doing this the calculation becomes easier and will reduce confusion of numbers.