Standard Deviation Practice (together)
a) Find the standard deviation for the following ages of people on a city bus.
16, 19, 15, 22, 14, 20, 19
b) Explain what the standard deviation means in the context of the situation and provide a range of ages in which most of the people on the bus fall into.
Solution
1
Try These (to be collected)
1) a) Find the standard deviation for the following tree heights (cm).
95, 135, 124, 98, 147, 152, 121
b) Explain what the standard deviation means in the context of the situation and provide a range of heights in which most trees will fall into.
2) a) Find the standard deviation for the following science test marks.
83, 71, 64, 46, 92, 66, 75
b) Explain what the standard deviation means in the context of the situation and provide a range of test marks in which most test scores will fall into.
Solution
1) a) i) Mean = (95 + 135 + 124 + 98 + 147 + 152 + 121)/7 = 872/7 = 124.57142 = 125
ii) Data Values
95
135
124
98
147
152
121
Deviation from Mean
30
­10
1
27
­22
­27
4
Squared Deviation
900
100
1
729
484
729
16
iii) Squared Deviation Mean = 900+100+1+729+484+729+16
7
= 2959/7 = 422.71428 = 423
iv) 423 = 20.566963 = 21
b) The standard deviation is 21 cm and it means that most tree heights are 21 cm away from the mean of 125 cm. So, most tree heights from the data fall between 104 cm and 146 cm.
2
Solution
2) a) i) Mean = 83 + 71 + 64 + 46 + 92 + 66 + 75 = 497 = 71 7
7
ii) Data Values
83
71
64
46
92
66
75
Deviation from Mean
­12
0
7
25
­21
5
­4
Squared Deviation
144
0
49
625
441
25
16
iii) Squared Deviation Mean = 144 + 0 + 49 + 625 + 441 + 25 + 16
7
= 1300/7 = 185.71428 = 186
iv) 186 = 13.638181 = 14 %
b) The standard deviation is 14% which means that most test scores on the science test are 14% away from the mean of 71%. This means that most students in the class scored between 57% and 85% on the science test. 3