Question

(a)You just wrapped up a traffic study during your summer internship. For your study you counted cars headed north through a busy intersection. This study occurred on weekdays over a two week period. Thus you recorded 10 data points of the daily traffic count for that day. The results were as follows: 345, 320, 376, 352, 351, 343, 364, 348, 332, 339. Please determine by hand (No Excel) the mode, median, mean and standard deviation of this 10 score data set.

(b)plot the scores by the stem and leaf method. What is the approximate distribution shape of the data? Did the graphical representation of the data match the central tendency predicted by the mean?

Answer 1

1) mean

=3470/10

mean=347

2) Median

Firstly arrange data in ascending order then we calculate median value

320
332
339
343
345
348
351
352
364
376

median = {(5th obs)+(6th obs)}/2

=(345+348)/2=346.5

Median =346.5

3) Mode

here no any value reprated so we dont find mode value for this given data

Mode=N/A

4) standard deviation

so firstly we find variance

variance={(345-347)^2+(320-347)^2+(376-347)^2+.....+(339-347)^2)}/10-1

=245.5556

standard deviation=sqrt(var)

=sqrt(245.5556)

standard deviation=15.6702

B)

by using stem and leaf method

v Stem-and-Leaf Plot

Frequency Stem & Leaf

1.00 32 . 0
2.00 33 . 29
3.00 34 . 358
2.00 35 . 12
1.00 36 . 4
1.00 Extremes (>=376)

Stem width: 10
Each leaf: 1 case(s)