Determine: (i) The upper and lower values or speed limits for installing speed regulation signs at this road stretch and (ii) the design speed for checking the geometric design elements of the highway.

This problem may be solved in three stages. First a frequency distribution table is prepared using the given spot speed data; next the cumulative frequency distribution diagram is drawn and finally the appropriate values are obtained from the graph.

(1) Frequency distribution and cumulative frequency values of spot speeds

Frequency distribution table of spot speed data is prepared. Column no. 2 of the table represents the average values of the different speed ranges. Column no.3 gives the no of vehicles observed in each speed range and is represented as the frequency f. The frequency values expressed as a percentage of the total no of vehicles observed in all the speed ranges is given in the column no 4. The cumulative percent of vehicles travelled at or below the different speeds are given in column o 5.

(2) Cumulative spot speed distribution diagram

The cumulative spot speed distribution diagram is drawn by plotting the mid speed values of the column 2 of the table on the X-axis and the % cumulative frequency values of vehicles travelling at or below the specific speed given column 5 of the table on the Y-axis as shown in fig. From the cumulative speed distribution diagram, the following values are obtained.

(3) Desired speed values

(a) Upper speed limit for regulation = $85^{th}$ percentile speed = 60 kmph

(b) Lower speed limit for regulation = $15^{th}$ percentile speed = 30 kmph

(c) Speed to check geometric design elements = $98^{th}$ percentile speed = 84 kmph