Answer:
[tex]\boxed{50.41}[/tex]
Step-by-step explanation:
The formula for estimating the mean from grouped data is:
[tex]\text{Median} = L + \dfrac{\frac{n}{2} - B}{f}\times w[/tex]
where
L = lower boundary of class (group) containing the median
n = total number of values
B = cumulative frequency of classes before the median class
f = frequency of median class
w = class width
In our distribution,
n = 11 + 21 + 33 + 23 + 12
n = 100
The median is the middle value, which in our case is about the 50th term.
The median is in the 40-59 class, so the median class is the 40-59 class.
The class width is
w = 60 - 40
w = 20
The frequency of the median class is
f = 33
The cumulative frequency of classes before the median is
B = 11 + 21
B = 32
We say that the median class is 40 - 59, but it's really 39.5 - 59.5. Thus, the lower bound of the median class is
L = 39.5
We now have enough information to calculate the median.
[tex]\begin{array}{rcl}\\\text{Median}& = & L + \dfrac{\frac{n}{2} - B}{f}\times w \\\\& = & 39.5 + \dfrac{\frac{100}{2} - 32}{33}\times 20\\ \\& = &39.5 + \dfrac{50 - 32}{33}\times 20\\\\& = &39.5 + \dfrac{18}{33}\times 20 \\\\& = &39.5 + 10.91 \\& = & \mathbf{50.41}\\\end{array}\[/tex]
[tex]\text{The median number of texts sent per day is }\boxed{\mathbf{50.41}}[/tex]
