Question

Tanya is investigating the daily mean windspeeds in Leeming. 1 The grouped frequency table below summarises the daily mean windspeeds in Leeming from 22nd September to 31st October 1987. Windspeed (nearest kn) Frequency 0-4 17 5 -8 14 9-12 13-18 a) Tanya says that the class width of the 5 -8 category is 3 kn. Explain why she is not correct. b) Use the data to estimate the lower quartile (Q), upper quartile (Q,) and interquartile range (IQR) for the daily mean windspeeds over this periocd

Answer 1

(a) The class width of the 5 - 8 category is actually 4 km as the given data is a discontinuous graphed data, so after adjusting with (10.5) to make it a continuous data we can see the width of the said category is (8.5 - 4.5) = 4 km (b) Estimating lower quartile(Q_1): - Q_1 = L_q_1 + sigma f/4 - F_8-1/fQ_1 times C_Q_1 here Q_1 = class is 0 - 4.5 where, LQ_1 = lower limit of Q_1- class = sigma f/4 = 40/4 = 10 F_Q_1 - 1 = commutative frequency of the class preceding to Q_1 - class = 0 (as there is not such class) f_Q_1 = frequency of Q_1 class = 17 C_Q_1 = width of the q_1 class = 4.5 therefore Q_1 = 0 + 10 - 0/ 17 times 4.5 tilde equation 2.65 Estimating upper quartile: - Q_3 = L_Q_3 + 3 sigma f/4 - F_Q_3 -1/f_q_3 times C_Q_3 where LQ_3