Question

find the median and mean of the data set below:
28, 7, 14, 27, 34, 38, 34
answer attempt 1 out of 2
median =
mean =

Explanation:

Step1: Find the Median

First, we need to order the data set from least to greatest. The data set is \(28, 7, 14, 27, 34, 38, 34\). When we order it, we get \(7, 14, 27, 28, 34, 34, 38\). Since there are 7 (an odd number) of data points, the median is the middle value, which is the 4th value. So the median is \(28\).

Step2: Find the Mean

To find the mean, we sum all the values and divide by the number of values. The sum of the data set is \(7 + 14 + 27 + 28 + 34 + 34 + 38\). Let's calculate that: \(7+14 = 21\), \(21+27 = 48\), \(48+28 = 76\), \(76+34 = 110\), \(110+34 = 144\), \(144+38 = 182\). There are 7 data points, so the mean is \(\frac{182}{7}=26\)? Wait, no, wait: \(7 + 14 = 21\), \(21+27 = 48\), \(48+28 = 76\), \(76+34 = 110\), \(110+34 = 144\), \(144+38 = 182\). Then \(182\div7 = 26\)? Wait, no, 726=182? Wait 720=140, 7*6=42, 140+42=182. Wait but let's check the data set again: 7,14,27,28,34,34,38. Wait 7+14=21, 21+27=48, 48+28=76, 76+34=110, 110+34=144, 144+38=182. Yes, 182 divided by 7 is 26? Wait no, wait 38+34=72, 72+34=106, 106+28=134, 134+27=161, 161+14=175, 175+7=182. Yes, 182/7=26. Wait but let's check the median again. The ordered data is 7,14,27,28,34,34,38. The middle term is the 4th term, which is 28. So median is 28, mean is 26? Wait no, wait 28+34+34+38= 28+34=62, 62+34=96, 96+38=134. 7+14+27=48. 134+48=182. 182/7=26. Yes.

Wait, but let me recheck the mean calculation. Sum of all numbers: 7 + 14 = 21; 21 + 27 = 48; 48 + 28 = 76; 76 + 34 = 110; 110 + 34 = 144; 144 + 38 = 182. Number of data points: 7. So mean is 182 / 7 = 26. Median: ordered data is 7,14,27,28,34,34,38. The middle value (since n=7, which is odd) is at position (7+1)/2 = 4th term. The 4th term is 28. So median is 28, mean is 26.

Wait, but wait, maybe I made a mistake in the mean. Let's add again: 7,14,27,28,34,34,38. 7+14=21; 21+27=48; 48+28=76; 76+34=110; 110+34=144; 144+38=182. 182 divided by 7: 7*26=182. Yes, that's correct. So mean is 26, median is 28.

Answer:

Median = \(\boxed{28}\), Mean = \(\boxed{26}\)