Respuesta :
Answer:
Mean = 30, Median = 29.5, Range = 9 and Mid-range = 29.5.
Step-by-step explanation:
We are given that a local doctor’s office logged the number of patients seen in one day by the doctor for ten days.
Arranging the given data in ascending order we get;
24, 25, 27, 27, 28, 31, 33, 35, 35, 35.
(a) Mean is calculated by using the following formula;
Mean, [tex]\bar X[/tex] = [tex]\frac{\text{Sum of all values}}{\text{Total number of observations}}[/tex]
= [tex]\frac{27+ 31+ 27+ 35+ 35+ 25+ 28+ 35+ 33+ 24}{10}[/tex]
= [tex]\frac{300}{10}[/tex] = 30
So, the mean of the given data is 30.
(b) For calculating the median, we have to first have to observe that the number of observations (n) in the data is even or odd.
- If n is odd, then the formula for calculating median is given by;
Median = [tex](\frac{n+1}{2})^{th} \text{ obs.}[/tex]
- If n is even, then the formula for calculating median is given by;
Median = [tex]\frac{(\frac{n}{2})^{th} \text{ obs.}+ (\frac{n}{2}+1)^{th} \text{ obs.} }{2}[/tex]
Here, the number of observations is even, i.e. n = 10.
So, Median = [tex]\frac{(\frac{n}{2})^{th} \text{ obs.}+ (\frac{n}{2}+1)^{th} \text{ obs.} }{2}[/tex]
= [tex]\frac{(\frac{10}{2})^{th} \text{ obs.}+ (\frac{10}{2}+1)^{th} \text{ obs.} }{2}[/tex]
= [tex]\frac{(5)^{th} \text{ obs.}+ (6)^{th} \text{ obs.} }{2}[/tex]
= [tex]\frac{28+31}{2}[/tex]
= [tex]\frac{59}{2}[/tex] = 29.5
So, the median of the data is 29.5.
(c) The range of the data is given by = Highest value - Lowest value
= 35 - 24 = 9
So, the range of the data is 9.
(d) Mid-range of the data is given by the following formula;
Mid-range = [tex]\frac{\text{Highest value}+\text{Lowest value}}{2}[/tex]
= [tex]\frac{35+24}{2}[/tex] = 29.5
