Question

question 2
calculate the mean and median of the dataset shown.
{202, 199, 223, 199, 223, 256, 301, 199}
mean = 225.25, median = 199
mean = 212.5, median = 225.25
mean = 199, median = 212.5
mean = 225.25, median = 212.5

Explanation:

Step1: Calculate the mean

First, find the sum of the dataset: \(202 + 199 + 223 + 190 + 223 + 256 + 301 + 199\)
\(= (202 + 199) + (223 + 190) + (223 + 256) + (301 + 199)\)
\(= 401 + 413 + 479 + 500\)
\(= 401 + 413 = 814\); \(814 + 479 = 1293\); \(1293 + 500 = 1793\)
There are 8 data points, so the mean is \(\frac{1793}{8} = 224.125\)? Wait, no, let's recalculate the sum:
202 + 199 = 401; 401 + 223 = 624; 624 + 190 = 814; 814 + 223 = 1037; 1037 + 256 = 1293; 1293 + 301 = 1594; 1594 + 199 = 1793. Wait, 1793 divided by 8: 8*224 = 1792, so 1793/8 = 224.125? But the option has 225.25. Wait, maybe I miscalculated the sum. Let's add again:
202, 199, 223, 190, 223, 256, 301, 199.
202 + 199 = 401; 401 + 223 = 624; 624 + 190 = 814; 814 + 223 = 1037; 1037 + 256 = 1293; 1293 + 301 = 1594; 1594 + 199 = 1793. Wait, 1793/8 = 224.125. But the option has 225.25. Wait, maybe the dataset is different? Wait, maybe I misread the numbers. Let's check again: {202, 199, 223, 190, 223, 256, 301, 199} – no, that's 8 numbers. Wait, maybe the user made a typo, or I miscalculated. Wait, let's check the median first.

Step2: Calculate the median

First, sort the dataset: 190, 199, 199, 202, 223, 223, 256, 301.
There are 8 numbers (even), so the median is the average of the 4th and 5th terms.
4th term: 202; 5th term: 223.
Median = \(\frac{202 + 223}{2} = \frac{425}{2} = 212.5\).

Now, recalculate the mean. Wait, maybe I added wrong. Let's add all numbers:
190 + 199 + 199 + 202 + 223 + 223 + 256 + 301.
190 + 199 = 389; 389 + 199 = 588; 588 + 202 = 790; 790 + 223 = 1013; 1013 + 223 = 1236; 1236 + 256 = 1492; 1492 + 301 = 1793. Wait, 1793/8 = 224.125. But the option has 225.25. Wait, maybe the dataset is {202, 199, 223, 190, 223, 256, 301, 199} – no, maybe a number is wrong. Wait, maybe 301 is 302? Let's check: 1793 +1 = 1794, 1794/8 = 224.25. No. Wait, maybe the original dataset is different. Wait, the option has mean 225.25, which is 1802/8 = 225.25. So 1802 - 1793 = 9. So maybe one of the numbers is 9 more. For example, if 190 is 199, then sum is 1793 +9=1802. Let's check: 199 instead of 190. Then the dataset is {202, 199, 223, 199, 223, 256, 301, 199}. Sum: 202 + 1993 + 2232 + 256 + 301. 1993=597; 2232=446; 202 + 597 = 799; 799 + 446 = 1245; 1245 + 256 = 1501; 1501 + 301 = 1802. Then mean is 1802/8 = 225.25. Ah, maybe a typo in the dataset, 190 should be 199. Then the sorted dataset would be 199, 199, 199, 202, 223, 223, 256, 301. Wait, no, original dataset has 190. But according to the options, the median is 212.5, which matches our calculation when the dataset is sorted as 190, 199, 199, 202, 223, 223, 256, 301 (median 212.5). And the mean in the option is 225.25, which would be if the sum is 1802. So maybe there's a typo, but the option with median 212.5 and mean 225.25 is the last option: "mean = 225.25, median = 212.5". So that's the answer.

Answer:

mean = 225.25, median = 212.5