statistics

Question

The diameters of a sample of 400 washers produced by a machine are summarised in table

1 below:

Diameter (millimeters)		Number of washers
	30 -under 40	10
	40 –under 50	50
	50 –under 60	55
	60 –under 70	79
	70 –under 80	68
	80 –under 90	60
	90 –under 100	50
100 –under 110		20
110 –under 120		8
Total		400

Table 1

Required:

 

1.1	Draw a Histogram of the above grouped frequency distribution.
1.2	Draw the upward sloping ogive of the above grouped frequency distribution.
1.3	Calculate mode and the median of the above data
1.4	Establish the value of the Standard Deviation of the above grouped frequency
	distribution using appropriate computational formulae.

Answer 1

1.1 HISTOGRAM

1.2 OGIVE CURVE

1.3 MODE is the most frequent value=60 to under 70; MEDIAN is the central datum: the central datum is 200 in the ordered set of data, which is 70-80. [An estimate from the ogive curve gives us about 71 (70+10*6/68).]

1.4 To find the SD we need to calculate the mean. I did this be taking the midrange value of the diameter and multiplying by the frequency for each group. For example, 30-40 has a midrange value of 35mm. Multiply this by the frequency: 35*10=350. I then took the sum of all such products: 28730 and divided by the data size 400 to give 71.825mm as the mean. This is close to the median (71mm).

If we use the median as the mean, we can calculate the difference between each midrange value and the mean, square it and multiply by the frequency. We then add all these values together and divide by 400. When we do this we get the variance=360.85. The square root of this is the SD=19mm (approximately).

I don't know if this is the right answer, but I hope it helps.