Calculating Mean, Range, and Standard Deviation (Math Problem Sample)
no format, just answer and complete the questions in order
source..Name_____________________________
Classwork #2
Module 4 Part 3 & Module 4 Part 4
1. The following data represents the length of eruption for a random sample of eruptions at the Old Faithful geyser in Yellowstone National Park.
108
108
99
105
103
103
94
107
99
106
90
104
110
110
103
109
109
111
102
101
110
102
105
110
106
104
104
100
103
101
125
90
113
116
95
105
103
101
100
101
102
110
92
108
Use the data to calculate the following:
a. Mean - 104.25b. Median – 104
c. Range – 35d. Q1 – 101
e. Q3 – 108.5f. IQR – 7.5
2. Create a boxplot of the data from question #1.
3. Answer the following questions using the box plot below.
a. Give the 5-number summary (approximate) of actors.
Min - 30
Q1 -37
Median - 43
Q3 - 50
Max - 76
b. Give the 5-number summary (approximate) of actresses.
Min – 22
Q1 – 33
Median – 35
Q3 – 42
Max – 49
c. Which distribution has the higher measure of center?
Actors
d. Which distribution has the higher ranger?
Actors
Module 4 Part 5
1. What is the notation (symbol) for the population standard deviation and population variance?
Population standard deviation – σ
Population variance – σ2
2. What is the notation (symbol) for the sample standard deviation and sample variance?
Sample standard deviation – s
Sample variance – s2
3. Let’s calculate the standard deviation by hand using a simple data set.
17, 12, 9, 5, 21, 14, 7, 11
Mean=17+12+9+5+21+14+7+118=968=12
a. Calculate the range of the data set.
Range = 21 – 5 = 16
Range = 16
b. Compute the standard deviation, by hand, using the table below.
data values (xi)
mean (x)
deviations from mean (xi-x)
Deviations squared xi-x2
5
12
-7
49
7
12
-5
25
9
12
-3
9
11
12
-1
1
12
12
0
0
14
12
2
4
17
12
5
25
21
12
9
81
c. Take the sum of the deviations squared column.
Sum = 49+25+9+1+0+4+25+81
Sum = 194
d. Take the sum you found in part (c) and divide it by the number of observations minus one (n–1).
s2=1947=27.7143
e. Finally, take the value from part (d) and take the square root. This gives you the sample standard deviation.
s=27.7143=5.2644
f. What is the value from part (d) called?
The sample standard deviation.
3. The following data set represents the weight of grams of a random sample of 50 plain M&M candies.
0.87
0.88
0.82
0.90
0.90
0.84
0.84
0.91
0.94
0.86
0.86
0.86
0.88
0.87
0.89
0.91
0.86
0.87
0.93
0.88
0.83
0.95
0.87
0.93
0.91
0.85
0.91
0.91
0.86
0.89
0.87
0.84
0.88
0.88
0.89
0.79
0.82
0.83
0.90
0.88
0.84
0.93
0.81
0.90
0.88
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