2. From the data given below calculate the value of first and third quartiles, second and ninth deciles and forty-fifth and fifty-seventh percentiles. Height in centimeters Number of students Cumulative frequency 161-167 79 79 167-173 92 171 173-179 60 231 179-185 22 253 185-191 5 258 191-197 2 260 Total 260

Hello student,
First of all, let us tabulate the data in a systematic form:
Class Interval f cf
161-167 79 79
167-173 92 171
173-179 60 231
179-185 22 253
185-191 5 258
191-197 2 260
Q₁ = 161 + 6/79 .(65-0)
= 165.93
Q₃ = 161 + 6/79 .(65-0)
= 165.93
D₂ is given by 52^nd value lying in C.I 161-167 and D₉ lies in C.I. 179-185.
So, D₂ = 161 + 6/79 .(52-0)
= 164.95
D₉ = 179 + 6/22 .(234-231)
= 179.82
Similarly,
P₄₅ = 167 + 6/92 .(117-79-0)
= 169.47
P₅₇ = 167 + 6/92 .(148-79)
= 171.5