6.
9
a. 39 b. 47 c. 49 d. 37
The mean = The sum of all the values ÷ The number of values. 18 + 15 + 22 + 18 + 25 + 19 + 23 = 140 : Number of values = 7 Mean = 140 ÷ 7 = 20
Mean = (12+14+25+10+25+15+11)/7 = 112/7 = 16
Remember what each of these terms represent. Mean = Mathematical Average Median = Middle value (exactly half of values are above and below) Mode = Most frequent value There are multiple possible answers, however here is one: 13, 13, 15, 15, 19 The mean is: (13 + 13 + 15 + 15 + 19)/5 = 75/5 = 15 The middle value (the median) is 15. Another way to say this is that, if we were to list all the values as shown above there are two before 15 and two after 15; therefore the median is 15. In this data set the value 13 occurs twice, 15 occurs twice, and 19 occurs once. Both 13 and 15 occur the most frequently therefore they are both the mode.
39
a data set in this case can be any collection of numbers you choose. Say we define Set A = {1,2,3,4,5} The Median for Set A is 3. The mean is the sum of the numbers divided by 5 in this case. 15/5 = 3 is the mean of Set A.
Whatever you like. The median value for each of the following three sets is 10. For the set {1, 9, 11, 12}. the mean is 8.25, smaller than the median. For the set {1, 9, 15, 15}. the mean is 10, the same as the median. For the set {1, 9, 15, 16}. the mean is 10.25, larger than the median.
15
15
9
a. 39 b. 47 c. 49 d. 37
12
38+46+15+27+36 = 162 and 162/5 = 32.4 which is the mean average
The one where the highest and lowest members differ by 15.
The median is the mean of the middle two. For example, find the median of the set {1, 3, 4, 6, 9, 10, 15, 20}. There are 8 items in the data set, so the median is the mean of the middle two. The middle two are the 4th and 5th data items: 6 & 9 median = mean of 6 & 9 = (6 + 9)/2 = 7.5
The mean will move up by 5 also as the whole data set has shifted up by 5, hence the mean is 105. The spread of the data has not changed, its just been "lifted up and moved along 5" and so the standard deviation is the same, i.e. 15 Hope this helps