Stem-and-Leaf Display: dowels Stem-and-leaf of dowels N 30 1 50 7 2 51 0 652 679

Question

Stem-and-Leaf Display: dowels Stem-and-leaf of dowels N 30 1 50 7 2 51 0 652 6799 12 53 044569 (5) 54 02467 13 55 03578 856 12358 3 57 59 1 58 5 Leaf Unit = 0.01 a.) What is the median dowel length b.) What are the smallest and largest dowel lengths c.) Two thirds of the dowel lengths are between what 2 values d.) What fraction of the dowel length is below 5.5 e.) Circle the one that best fits The mean and median are approximately equal The mean is much greater than the median -The mean is much smaller than the median

Explanation / Answer

a)

Since there are 30 data values so median will be average of 15th and 16th data values. The 15th data value is 5.44 and 16th data value is 5.46. So median is

Median = (5.44+ 5.46) / 2 = 5.45

(b)

The smallest value is: 5.07

The largest value is: 5.85

(c)

There are 30 data values so 2/3 of data values means (2/3) *30 = 20. The starting 20 data values lies between 5.07 and 5.55.

(d)

Out of 30 data values, 17 data values are less than 5.50. So fraction of dowel length below 5.5 is

17 / 30 = 0.567

Hence, required fraction is 0.567.

(e)

Stem and leaf display shows the distribution of dowel length is approxiamtely symmetric so mean and median should be approxiamtely equal.

First option is correct.

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