Visits by seven patients in a month are as follows: $3, 5, 2, 7, 1, 4, 5$
Answer (2)
Calculate the mean: Sum the visits and divide by the number of patients, resulting in approximately 3.86 .
Determine the median: Sort the visits and find the middle value, which is 4 .
Identify the mode: Find the most frequent visit number, which is 5 .
Compute the range: Subtract the minimum visit number from the maximum, resulting in 6 .
Calculate the standard deviation: Measure the spread of the data around the mean, resulting in approximately 1.88 .
Explanation
Problem Analysis We are given the number of visits by seven patients in a month: 3, 5, 2, 7, 1, 4, 5. We need to analyze this data by calculating the mean, median, mode, range, and standard deviation.
Calculating the Mean First, let's calculate the mean. The mean is the sum of all the values divided by the number of values. So, we have: ( 3 + 5 + 2 + 7 + 1 + 4 + 5 ) /7 = 27/7 ≈ 3.86 Thus, the mean is approximately 3.86.
Finding the Median Next, let's find the median. To find the median, we first need to sort the data in ascending order: 1, 2, 3, 4, 5, 5, 7. Since there are 7 values (an odd number), the median is the middle value, which is 4.
Determining the Mode Now, let's determine the mode. The mode is the value that appears most frequently in the data. In our data set (3, 5, 2, 7, 1, 4, 5), the number 5 appears twice, which is more than any other number. Therefore, the mode is 5.
Calculating the Range To find the range, we subtract the smallest value from the largest value. The largest value is 7, and the smallest value is 1. So, the range is: 7 − 1 = 6 Thus, the range is 6.
Calculating the Standard Deviation Finally, let's calculate the standard deviation. The standard deviation measures the spread of the data around the mean. First, we calculate the variance, which is the average of the squared differences from the mean. The mean is approximately 3.86. The variance is: 7 ( 3 − 3.86 ) 2 + ( 5 − 3.86 ) 2 + ( 2 − 3.86 ) 2 + ( 7 − 3.86 ) 2 + ( 1 − 3.86 ) 2 + ( 4 − 3.86 ) 2 + ( 5 − 3.86 ) 2 ≈ 7 0.7396 + 1.2996 + 3.4596 + 9.8596 + 8.1796 + 0.0196 + 1.2996 ≈ 7 24.8572 ≈ 3.551 Then, the standard deviation is the square root of the variance: 3.551 ≈ 1.88 Thus, the standard deviation is approximately 1.88.
Final Answer In summary, for the given patient visits data: the mean is approximately 3.86, the median is 4, the mode is 5, the range is 6, and the standard deviation is approximately 1.88.
Examples
Understanding patient visit patterns is crucial in healthcare management. For example, a clinic might use the mean number of visits to forecast staffing needs, the median to understand typical visit rates unaffected by outliers, and the mode to identify the most common visit frequency. The range helps in understanding the variability in patient visits, while the standard deviation quantifies the spread, aiding in resource allocation and quality improvement initiatives. By analyzing these statistics, healthcare providers can optimize their services and better meet patient needs.
The analysis of patient visits shows the mean is approximately 3.86, the median is 4, the mode is 5, the range is 6, and the standard deviation is approximately 1.88.
;
