Answer to Question #73383 in Statistics and Probability for Pradeep

Question

1. The following data are the measures of the diameters of 36 rivet heads in millimetres.
170.69 171.96 173.23 170.18 172.21 170.18 168.15 171.45 169.16
169.16 168.66 171.70 170.94 172.72 170.69 171.70 171.70 169.67
169.16 168.15 170.69 171.70 170.18 172.21 171.70 169.42 170.18
170.69 171.20 172.97 172.47 170.21 169.16 171.70 171.70 170.69
(i) Complete the table below.
Diameters Midpoint Frequency Cumulative Frequency
168.15  x 168.90
168.90  x 169.65
169.65  x 170.40
170.40  x 171.15
171.15  x 171.90
171.90  x 172.65
172.65  x 173.40
(ii) Based on the answer in (i), find the mean, median and mode. Then identify the shape
of the data and state your reason.
(iii) Based on the answer in (i), construct a histogram and a frequency polygon of the
measurement of the diameter of rivet heads on a same graph paper and axes. Then
identify the shape of the histogram.
(iv) Is the shape of distribution determined in (ii) can be supported by the shape of the
histogram? State your reason.