Objectives
Students will be able to:
- Calculate and describe the measures of center: mean and median
- Analyze the relationship of the mean and median to the shape of the data
=AVERAGE
.=AVERAGE
formula. If your data set is not too large, you can enter each value directly into the formula. Using this method, we write=AVERAGE(3.29 3.59, 3.79, 3.75, 3.99)
=AVERAGE(A1:A5)
Income (thousands of dollars) |
Frequency |
---|---|
$15 | 6 |
$20 | 8 |
$25 | 11 |
$30 | 17 |
$35 | 19 |
$40 | 20 |
$45 | 12 |
$50 | 7 |
=AVERAGE
to find the mean for this example, but it would require entering each repeated value individually. If the mean is all we need, then taking advantage of multiplication as repeated addition is the more straightforward way to go. We could also enter the frequency table and the calculation above in a spreadsheet.5 | 10 | 8 | 6 | 4 | 8 | 2 | 5 | 7 | 7 | 6 |
2 | 4 | 5 | 5 | 6 | 6 | 7 | 7 | 8 | 8 | 10 |
2 | 4 | 5 | 5 | 6 | 6 | 7 | 7 | 8 | 8 | 10 | 20 |
=MEDIAN
. Just like the spreadsheet function =AVERAGE
, we can either list the individual data values in the formula, or we can enter the data values into a row (or column) and use the row range (or column range) in the formula.=MEDIAN(A1:AK)
3.29 | 3.59 | 3.79 | 3.75 | 3.99 |
3.29 | 3.59 | 3.75 | 3.79 | 3.99 |
=MEDIAN(3.29, 3.59, 3.79, 3.75, 3.99)
7.50 | 25 | 10 | 10 | 7.50 | 8.25 | 9 | 5 | 15 | 8 | 7.25 | 7.50 | 8 | 7 | 12 |
10 | 12.75 | 7 | 9 | 9.75 | 6.5 | 12.5 | 12.5 | 8.75 | 17 | 10.5 | 2 |
15.2 | 18.8 | 19.3 | 19.7 | 20.2 | 21.8 | 22.1 | 29.4 |
3.49 | 3.51 | 3.51 | 3.51 | 3.52 | 3.54 | 3.55 | 3.58 | 3.61 |
Cost (Thousands of dollars) |
Frequency |
---|---|
15 | 3 |
20 | 7 |
25 | 10 |
30 | 15 |
35 | 13 |
40 | 11 |
45 | 9 |
50 | 7 |
openintro.org/stat/textbook.php?stat_book=aps
).Length of an email (Thousands of characters) |
Frequency |
---|---|
0 | 4 |
1 | 5 |
2 | 2 |
3 | 3 |
4 | 3 |
5 | 1 |
6 | 3 |
7 | 3 |
8 | 0 |
9 | 3 |
10 | 3 |
11 | 2 |
12 | 0 |
13 | 0 |
14 | 2 |
3 | 4 | 11 | 15 | 16 | 17 | 22 | 44 | 37 | 16 | 14 | 24 | 25 | 15 | 26 | 27 | 33 | 29 | 35 | 44 |
13 | 21 | 22 | 10 | 12 | 8 | 40 | 32 | 26 | 27 | 31 | 34 | 29 | 17 | 8 | 24 | 18 | 47 | 33 | 34 |
3 | 14 | 11 | 5 | 16 | 17 | 28 | 41 | 31 | 18 | 14 | 14 | 26 | 25 | 21 | 22 | 31 | 2 | 35 | 44 |
23 | 21 | 21 | 16 | 12 | 18 | 41 | 22 | 16 | 25 | 33 | 34 | 29 | 13 | 18 | 24 | 23 | 42 | 33 | 29 |
openintro.org/stat/textbook.php?stat_book=aps
).1,600 | 1,200 | 20,000 | 25,000 | 670 | 29,000 | 44,000 | 30,000 | 5,800 | 50,000 |
53,000 | 70,000 | 12,800 | 30,000 | 4,500 | 42,000 | 48,000 | 60,000 | 108,000 | 11,000 |
Non-players | Beginners | Tournament Players |
---|---|---|
22.1 | 32.5 | 40.1 |
22.3 | 37.1 | 45.6 |
26.2 | 39.1 | 51.2 |
29.6 | 40.5 | 56.4 |
31.7 | 45.5 | 58.1 |
33.5 | 51.3 | 71.1 |
38.9 | 52.6 | 74.9 |
39.7 | 55.7 | 75.9 |
39.7 | 55.7 | 75.9 |
43.2 | 55.9 | 80.3 |
43.2 | 57.7 | 85.3 |
onlinestatbook.com
, by David M. Lane, et al, used under CC-BY-SA 3.0.False Smile | Felt Smile | Miserable Smile | Nuetral Control |
---|---|---|---|
2.5 | 7 | 5.5 | 2 |
5.5 | 3 | 4 | 4 |
6.5 | 6 | 4 | 4 |
3.5 | 4.5 | 5 | 3 |
3 | 3.5 | 6 | 6 |
3.5 | 4 | 3.5 | 4.5 |
6 | 3 | 3.5 | 2 |
5 | 3 | 3.5 | 6 |
4 | 3.5 | 4 | 3 |
4.5 | 4.5 | 5.5 | 3 |
5 | 7 | 5.5 | 4.5 |
5.5 | 5 | 4.5 | 8 |
3.5 | 5 | 2.5 | 4 |
6 | 7.5 | 5.5 | 5 |
6.5 | 2.5 | 4.5 | 3.5 |
3 | 5 | 3 | 4.5 |
8 | 5.5 | 3.5 | 6.5 |
6.5 | 5.5 | 8 | 3.5 |
8 | 5 | 5 | 4.5 |
6 | 4 | 7.5 | 4.5 |
6 | 5 | 8 | 2.5 |
3 | 6.5 | 4 | 2.5 |
7 | 6.5 | 5.5 | 4.5 |
8 | 7 | 6.5 | 2.5 |
4 | 3.5 | 5 | 6 |
3 | 5 | 4 | 6 |
2.5 | 3.5 | 3 | 2 |
8 | 9 | 5 | 4 |
4.5 | 2.5 | 4 | 5.5 |
5.5 | 8.5 | 4 | 4 |
7.5 | 3.5 | 6 | 2.5 |
6 | 4.5 | 8 | 2.5 |
9 | 3.5 | 4.5 | 3 |
6.5 | 4.5 | 5.5 | 6.5 |
Shoe Size | Frequency |
---|---|
5 | 4 |
6 | 4 |
7 | 6 |
8 | 6 |
9 | 5 |
openintro.org/stat/textbook.php?stat_book=aps
)openintro.org/stat/textbook.php?stat_book=aps
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