# 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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