Question

You are the Industrial Engineering technologist employed by the JMPD and your supervisor has asked you to determine the most desirable setting for a series of three traffic signals on a two- kilometer strip of access road into Braamfontein. Applying your knowledge of work-study, you then devise a timing system to enable you to observe the number of vehicles going through all three signals without stopping or vehicles rushing a yellow signal. The data you collected is presented in the table below: Boundaries Midpoint Frequency 15.5-18.5 17 12 18.5-21.5 20 18 21.5-24.5 23 10 24.5-27.5 26 13 27.5-30.5 29 20 30.5-33.5 32 8 33.5-36.5 35 2 36.5-39.5 38 1 Compute the following: a) Average (5) (5) b) Three (3) Standard Deviation c) Variance for data d) The percentage of cars going through the signals during the 22nd and 29th time setting (8) (2) 528

Answer 1

In part (a),

               Total frequency = 12+18+10+13+20+8+2+1= 84

AVERAGE= {Sum of (midpoint$\times$frequency) } $\div$ total frequency

               = (17$\times$12 + 20$\times$18 + 23$\times$10 + 26$\times$13 + 29$\times$20 + 32$\times$8 + 35$\times$2 + 38$\times$1)$\div$84

               = 2076$\div$84 = 24.7143 ......................          (ANSWER)

In part (c),

VARIANCE ={Sum of (frequency$\times$(midpoint-average)^2)}$\div$ total frequency

                 ={12$\times$(17-24.7143)^2 + 18$\times$(20-24.7143)^2 + 10$\times$(23-24.7143)^2 + 13$\times$(26-24.7143)^2 + 20$\times$(29-24.7143)^2 +

                     8$\times$(32-24.7143)^2 + 2$\times$(35-24.7143)^2 + 1$\times$(38-24.7143)^2}$\div$84

                = 2345.1429 $\div$ 84= 27.9184.....................          (ANSWER)

In part (b),

STANDARD DEVIATION = Square root of variance

                                     = 5.2838 ..............................        (ANSWER)

In part (d),

The percentage of cars going through signals during 22nd and 29th time setting is

percentage during 22nd time = (frequency$\div$total frequency) $\times$ 100

                                              = (10$\div$84) $\times$ 100 = 11.9 ............................         (ANSWER)

percentage during 29th time = (frequency$\div$total frequency) $\times$ 100

                                             = (20$\div$84) $\times$ 100 = 23.8 ................................       (ANSWER)