Mathematics Term 1 Block 6 Assignment Questions
Note: Please provide the formulae in your calculations
1. The following are the heights in centimetres of 24 people.
(a) Complete the following frequency distribution table.
Height Mid-
height ( x )
Tally
Frequency ( f )
.f x x x− 2
( )x x− 2
.( )f x x−
145 –149 147 II 2 294 -18.75 351.5625 703.125
150 –154 152 IIII 4 608 -13.75 189.0625 756.25
155 –159 157 III 3 471 -8.75 76.5625 229.6875
160 –164 162 I 1 162 -3.75 14.0625 14.0625
165 –169 167 IIII 4 668 1.25 1.5625 6.25
170 –174
175 –179
180 –184
Totals
Use the above information to: (b) Construct a histogram showing these results.
156 162 174 183 177 169 153 150
151 172 158 171 169 174 180 183
184 154 182 148 168 149 167 159
(c) Calculate the mean (for grouped data) and the modal class.
(d) Calculate the variance and the standard deviation for grouped data to 4 significant figures. Check your answers with a calculator.
2. Find the mean, median, range, quartiles and the inter-quartile range for each of the following sets of data. (There is no need to group the data.)
(a) 25, 22, 24, 21, 20, 18, 16, 19, 24, 19, 18, 17, 20, 21, 22. (b) 29, 28, 27, 30, 31, 32, 34, 31, 30, 28, 26, 35, 26, 31, 33, 30, 31, 25.
3. Complete the following table and use the information to find the mean,
median and standard deviation (to 3 significant figures) for the distribution.
x f .f x x x− 2( )x x− 2.( )f x x−
3 1 3 -4 16 16
4 2 8 -3 9 18
5 3 15 -2 4 12
6 5 30 -1 1 5
7 7 49 0 0 0
8 6
9 3
10 3
Totals:
