Let's first analyze the provided data set and see the necessary calculations before and after the change.
Original Data Set: 294, 402, 429, 437, 458, 486, 517, 533, 551, 573
- Median:
- The median is the middle value of an ordered data set. In a set with an even number of values, the median is the average of the two middle values.
- Here, there are 10 data points. The two middle values are the 5th and 6th values (458 and 486).
\[ \text{Median} = \frac{458 + 486}{2} = \frac{944}{2} = 472 \]
- Mean:
- The mean is calculated by adding all the numbers and dividing by the count of the numbers.
\[ \text{Sum of the original data} = 294 + 402 + 429 + 437 + 458 + 486 + 517 + 533 + 551 + 573 = 4580 \]
\[ \text{Mean} = \frac{4580}{10} = 458.0 \]
New Data Set (with 573 changed to 403): 294, 402, 403, 429, 437, 458, 486, 517, 533, 551
- New Median:
- Now, we find the new median with the updated data set. The two middle values remain the same indices in a sorted list of 10 values (5th and 6th).
The 5th and 6th values are now 437 and 458.
\[ \text{New Median} = \frac{437 + 458}{2} = \frac{895}{2} = 447.5 \]
- New Mean:
- We'll calculate the new mean with the updated data set.
\[ \text{Sum of the new data} = 294 + 402 + 403 + 429 + 437 + 458 + 486 + 517 + 533 + 551 = 4510 \]
\[ \text{New Mean} = \frac{4510}{10} = 451.0 \]
Now let's answer the questions:
(A) What happens to the median?
- The original median was 472, and the new median is 447.5. So the median decreases.
(B) What happens to the mean?
- The original mean was 458.0, and the new mean is 451.0. So the mean also decreases.