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The numbers of trading cards owned by 10 middle-school students are given below.

(Note that these are already ordered from least to greatest.)
294, 402, 429, 437, 458, 486, 517, 533, 551, 573

Suppose that the number 573 from this list changes to 403. Answer the following.
(A) what happens to the median

(B) what happens to the mean

does it increase, decrease, stay the same, and by how much?

1 answer

Let's analyze the changes step by step after replacing the number 573 with 403 in the dataset.

Original List:

294, 402, 429, 437, 458, 486, 517, 533, 551, 573

New List (after changing 573 to 403):

294, 402, 403, 429, 437, 458, 486, 517, 533, 551

(A) What happens to the median?

The median is the middle value of a data set. When the numbers are ordered, if there is an even number of values (like in this case, where we have 10 numbers), the median is the average of the two middle values.

Original List Median:

  • The two middle values are the 5th and 6th numbers: 458 and 486.
  • Median = (458 + 486) / 2 = 944 / 2 = 472

New List Median:

  • The two middle values are now the 5th and 6th numbers: 437 and 458.
  • Median = (437 + 458) / 2 = 895 / 2 = 447.5

Conclusion: The median decreases from 472 to 447.5.

(B) What happens to the mean?

To find the mean, we calculate the sum of all the numbers and then divide by the number of values.

Original List Mean:

  • Sum = 294 + 402 + 429 + 437 + 458 + 486 + 517 + 533 + 551 + 573 = 4288
  • Mean = 4288 / 10 = 428.8

New List Mean:

  • New sum (after replacing 573 with 403) = 294 + 402 + 403 + 429 + 437 + 458 + 486 + 517 + 533 + 551
  • New sum = 4260
  • New mean = 4260 / 10 = 426.0

Conclusion: The mean decreases from 428.8 to 426.0.

Summary:

  • (A) The median decreases from 472 to 447.5.
  • (B) The mean decreases from 428.8 to 426.0.