In part (a),
Total frequency = 12+18+10+13+20+8+2+1= 84
AVERAGE= {Sum of (midpointfrequency) } total frequency
= (1712 + 2018 + 2310 + 2613 + 2920 + 328 + 352 + 381)84
= 207684 = 24.7143 ...................... (ANSWER)
In part (c),
VARIANCE ={Sum of (frequency(midpoint-average)^2)} total frequency
={12(17-24.7143)^2 + 18(20-24.7143)^2 + 10(23-24.7143)^2 + 13(26-24.7143)^2 + 20(29-24.7143)^2 +
8(32-24.7143)^2 + 2(35-24.7143)^2 + 1(38-24.7143)^2}84
= 2345.1429 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 = (frequencytotal frequency) 100
= (1084) 100 = 11.9 ............................ (ANSWER)
percentage during 29th time = (frequencytotal frequency) 100
= (2084) 100 = 23.8 ................................ (ANSWER)
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