Question

Help, pls!!!!

Answer 1

Answer:

20

Step-by-step explanation:

11, 12, 21, 23, 33

the middle number is 21

rounding off to 20

Answer 2

Answer:

$\boxed{50.41}$

Step-by-step explanation:

The formula for estimating the mean from grouped data is:  

$\text{Median} = L + \dfrac{\frac{n}{2} - B}{f}\times w$

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.

$\begin{array}{rcl}\\\text{Median}& = & L + \dfrac{\frac{n}{2} - B}{f}\times w \\\\& = & 39.5 + \dfrac{\frac{100}{2} - 32}{33}\times 20\\ \\& = &39.5 + \dfrac{50 - 32}{33}\times 20\\\\& = &39.5 + \dfrac{18}{33}\times 20 \\\\& = &39.5 + 10.91 \\& = & \mathbf{50.41}\\\end{array}$

$\text{The median number of texts sent per day is }\boxed{\mathbf{50.41}}$