Question

1. In a random sample, 10 employees at a local plant were asked to compute the distance they travel to work to the nearest tenth of a mile. The data is listed below.

1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8

a) Calculate the mean, median and the mode of the data.

b) Based on these numbers, what is the shape of the distribution?

c) Compute the range, standard deviation and variance of the data.

Answer 1

Arranging the data in ascending order

1	2	3	4	5	6	7	8	9	10
0.8	1.1	1.5	1.8	2.2	3.6	4.8	5.0	5.2	5.2

(a) Mean = Sum / Total = 31.2 / 10 = 3.12

Median: Since we have an even number of observations, the median is the average of the (n/2)th and the next data.

(n/2) th data = 10/2 = 5th data. Therefore average of the 5th and the 6th data = (2.2 + 3.6) / 2 = 5.8/2 = 2.9

Mode.: The data that occurs the maximum number of times = 5.2

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(b) If Mean = Median = Mode, then it is a symmetric distribution

Here Mode > Mean > Median and hence the distribution is skewed to the right.

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(c) The Range = Largest Value - Smallest Value = 5.2 - 0.8 = 4.4

The Variance = Sum of Squares / n - 1

#	X	Mean	(x - mean)2
1	1.1	3.120	4.080
2	5.2	3.120	4.326
3	3.6	3.120	0.230
4	5	3.120	3.534
5	4.8	3.120	2.822
6	1.8	3.120	1.742
7	2.2	3.120	0.846
8	5.2	3.120	4.326
9	1.5	3.120	2.624
10	0.8	3.120	5.382
Total	31.20		29.916

SS = 29.916

Therefore Variance = 29.916/9 = 3.324

Standard Deviation = SQRT(Variance) = SQRT(3.324) = 1.823

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