Question

A local doctor’s 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.

Answer 1

To find the mean, median, range, and midrange of the number of patients seen in the doctor's office over ten days, let's first list the numbers of patients seen:

**Data:** 27, 31, 27, 35, 35, 25, 28, 35, 33, 24

### Step 1: Calculate the Mean
The mean is calculated by summing all the numbers and dividing by the total count of the numbers.

\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
\]

Calculating the sum:

\[
27 + 31 + 27 + 35 + 35 + 25 + 28 + 35 + 33 + 24 = 27 + 31 + 27 + 35 + 35 + 25 + 28 + 35 + 33 + 24 = 30 \text{ (total) } = 30. 25 = 0.70 + 28 + 21 + 35 + 28 = 330
\]

Now, divide by the number of values (10):

\[
\text{Mean} = \frac{330}{10} = 33
\]

### Step 2: Calculate the Median
The median is the middle number when the data is sorted. If there is an even number of values, the median is the average of the two middle numbers.

First, let's sort the data:

**Sorted Data:** 24, 25, 27, 27, 28, 31, 33, 35, 35, 35

Since there are 10 values (even), the median will be the average of the 5th and 6th values.

5th value = 28
6th value = 31

\[
\text{Median} = \frac{28 + 31}{2} = \frac{59}{2} = 29.5
\]

### Step 3: Calculate the Range
The range is the difference between the highest and lowest values.

**Highest value:** 35
**Lowest value:** 24

\[
\text{Range} = \text{Highest value} - \text{Lowest value} = 35 - 24 = 11
\]

### Step 4: Calculate the Midrange
The midrange is the average of the highest and lowest values.

\[
\text{Midrange} = \frac{\text{Highest value} + \text{Lowest value}}{2} = \frac{35 + 24}{2} = \frac{59}{2} = 29.5
\]

### Summary of Results
- **Mean:** 33
- **Median:** 29.5
- **Range:** 11
- **Midrange:** 29.5