Red River of the North
Discharge, cubic feet per second
Daily Mean (Average) Values
March 1st to June 30th, 1997
Day March April  May June
1 2290 2750 49,100 10,100
2 2280 3190 46,300 9560
3 2350 6350 44,200 9170
4 2400 14,500 42,500 9070
5 2370 18,500 40,800 9140
6 2360 21,000 39,300 8800
7 2340 22,000 37,700 7970
8 2380 26,000 36,100 6950
9 2370 28,000 34,900 6270
10 2300 30,200 33,500 6020
11 2240 30,400 32,500 5860
12 2250 31,300 30,900 5640
13 2210 34,900 28,900 5450
14 2090 40,400 26,700 5360
15 2130 48,900 24,600 5280
16 2160 63,400 22,400 5220
17 2150 84,600 20,300 5200
18 2090 127,000 18,300 5140
19 2100 111,000 16,400 5110
20 2130 109,000 14,700 5060
21 2140 111,000 13,700 5010
22 2150 110,000 12,900 4980
23 2150 105,000 12,100 5060
24 2170 97,900 11,500 5770
25 2180 88,000 11,700 10,100
26 2190 78,400 12,400 16,100
27 2220 69,700 12,700 18,700
28 2250 63,000 12,400 18,900
29 2310 57,200 11,900 17,700
30 2410 52,700 11,300 15,800
31 2580 --- 10,600 ---
monthly 
mean:		 2250 56,210 24,490 8483
 
Part 1: Statistics:
Note: each of the underlined words below are linked to a more complete explanation of the term, plus some examples. 

1) The range of a set of data (numerical values) can be defined as the difference between the largest and smallest values in that set of data.  The range for the month of March is given below. Find the range of the water discharge for April, May, and June. 
March: 490 ft3/sec. May: 38,500 ft3/sec.
April: 124,250 ft3/sec. June: 13,920ft3/sec.
2) The median value of a set of data is the middle value, once the data is arranged in ascending order. The median value for March is given below.  Find the median value for April, May, and June. 
March: 2240 ft3/sec. May: 22,400 ft3/sec.
April: 50,800 ft3/sec. June: 6145 ft3/sec.
3) The first quartile of a set of data is the value in which 25% of the data is below it, 75% of the data is above it (once arranged in ascending order); the third quartile is the value in which 75% of the data is below it, 25% of the data is above it.  The first and third quartiles are given for the month of March.  Find the first and third quartiles for April, May, and June. 
March: 2150; 2350 ft3/sec. May: 12,400; 36,100 ft3/sec.
April: 26,000; 88,000 ft3/sec. June: 5220; 9560 ft3/sec.
4) A five number summary consists of the following information:  the minimum value, the maximum value, the median, the first quartile, and the third quartile  A five number summary can be represented graphically by a box plot.  The box plot for the month of March is shown here; on this page, draw in the box plots for April, May, and June.  Then answer the rest of the questions found on that sheet. 
answer key
Part 2: Means and Medians
Note: For this part (as well as part 1), it may be best to have students work in groups of 3 or 4.  The answers below for questions 2 - 7 are correct, but you should consider other answers if students can support their answer with sound reasoning.

1) How many days in each month are above or equal to the monthly mean discharge of the Red River?
 
March: 15 (so16 below mean) May: 14 (so 17 below mean)
April: 14 (so 16 below mean) June: 12 (so 18 below mean)
2) For the month of March, which is a better statistic to describe the average discharge of the Red River?
    a) mean
    b) median
    c) either would work well
    d) neither would work well

3) Support your answer for #2: Why is your answer the best choice?
 
 There is very little difference in the mean (2250) and the median (2240), plus there are almost as many days above and below the mean as the median.
 
4) For the month of April, which is a better statistic to describe the average discharge of the Red River?
    a) mean
    b) median
    c) either would work well
    d) neither would work well

5) Support your answer for #4: Why is your answer the best choice?
 
 Because the spread and range of the data during April was so wide (from 2750 to 127,000 with 6 days above 100,000), neither statistic works well for describing the average discharge (although choice c could be argued for based on the same reasoning).  You should explain to the students that sometimes a mean or median really doesn't desribe what is happening accurately.  You could use this example to help illustrate it: you have 21 students in class: 10 are 5 feet tall, 10 are 7 feet tall, and one is 6 feet tall.  Both the mean and median calculate to 6 feet, but that doesn't accurately describe the "average" height of your students.

6) For the month of June, which is a better statistic to describe the average discharge of the Red River?
    a) mean
    b) median
    c) either would work well
    d) neither would work well

7) Support your answer for #6: Why is your answer the best choice?
 
The mean was heavily influenced by the residual effects of the flood (in early June) and by a large thunderstorm late in the month.  As a result, only those 12 days are above the mean, 18 below.  The median more accurately represents the average flow.  A more extreme example can be demonstrated by asking all of the students to state their average annual salary; then announce that Leonardo DiCaprio (for example) was going to be a student in your class, and since he makes $30 million a year (or whatever number you wish to use), your classes' average salary is $1 million a year per student.  Obviously, in this case, the median would be a more accurate statistic.