Question

a local doctors office logged the number of patients seen in one day by the doctor for ten days. find the mean, median, range, and midrange of the number of patients seen in ten days.
27 31 27 35 35 25 28 35 33 24
calculate the mean, median, range, and midrange of the number of patients seen in ten days.
mean, 11; median, 29.5; range, 30; midrange, 29.5
mean, 29.5; median, 30; range, 29.5; midrange, 11
mean, 29.5; median, 11; range, 29.5; midrange, 30
mean, 30; median, 29.5; range, 11; midrange, 29.5

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$.
Here, $n = 10$ and $x_{i}$ are the data points: $27,31,27,35,35,25,28,35,33,24$.
$\sum_{i=1}^{10}x_{i}=27 + 31+27+35+35+25+28+35+33+24=300$.
$\bar{x}=\frac{300}{10}=30$.

Step2: Arrange the data in ascending order

$24,25,27,27,28,31,33,35,35,35$.
Since $n = 10$ (even), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$.
$x_{5}=28$ and $x_{6}=31$.
$M=\frac{28 + 31}{2}=29.5$.

Step3: Calculate the range

The range $R=\text{Max}-\text{Min}$.
$\text{Max}=35$, $\text{Min}=24$.
$R=35 - 24=11$.

Step4: Calculate the mid - range

The mid - range $MR=\frac{\text{Max}+\text{Min}}{2}$.
$MR=\frac{35+24}{2}=29.5$.

Answer:

Mean, 30; Median, 29.5; Range, 11; Midrange, 29.5 (the fourth option)