To find the difference between the median and the mean of the dataset, we first need to calculate both values.
Dataset:
{22, 26, 29, 27, 24, 22, 23, 20, 19, 28, 26, 18, 30, 31, 22, 23, 26, 29, 24, 21}
Step 1: Calculate the Mean
To calculate the mean, we sum all the values and divide by the number of values.
\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \]
Sum of values: 22 + 26 + 29 + 27 + 24 + 22 + 23 + 20 + 19 + 28 + 26 + 18 + 30 + 31 + 22 + 23 + 26 + 29 + 24 + 21 = 462
Number of values: 20 \[ \text{Mean} = \frac{462}{20} = 23.1 \]
Step 2: Calculate the Median
To find the median, we need to order the data from least to greatest:
Ordered dataset: {18, 19, 20, 21, 22, 22, 22, 23, 23, 24, 24, 26, 26, 26, 27, 28, 29, 29, 30, 31}
Since there are 20 values (an even number), the median will be the average of the 10th and 11th values.
10th value: 24 11th value: 24
\[ \text{Median} = \frac{24 + 24}{2} = 24 \]
Step 3: Calculate the Difference
Now we find the difference between the median and the mean:
\[ \text{Difference} = \text{Median} - \text{Mean} = 24 - 23.1 = 0.9 \]
Answer
The difference between the median and the mean of the dataset is 0.9.