Exploring data: graphs and numerical summaries
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# 5.2.2 Birth weights of infants with SIRDS

The data in Table 3 are the birth weights (in kg) of 50 infants suffering from severe idiopathic respiratory distress syndrome. There are two groups of infants: those who survived the condition (there were 23 of these) and those who, unfortunately, did not. The data have not been sorted, and it is not an entirely trivial exercise to do this by hand (though it is a task that a computer can handle very easily). The sorted data are given in Table 9.

## Table 9 Birth weights (in kg) of infants with severe idiopathic respiratory distress syndrome

1.030* | 1.300* | 1.720 | 2.090 | 2.570
1.050* | 1.310* | 1.750* | 2.200* | 2.600
1.100* | 1.410 | 1.760 | 2.200 | 2.700
1.130 | 1.500* | 1.770* | 2.270* | 2.730*
1.175* | 1.550* | 1.820* | 2.275* | 2.830
1.185* | 1.575 | 1.890* | 2.400 | 2.950
1.225* | 1.600* | 1.930 | 2.440* | 3.005
1.230* | 1.680 | 1.940* | 2.500* | 3.160
1.262* | 1.715 | 2.015 | 2.550 | 3.400
1.295* | 1.720* | 2.040 | 2.560* | 3.640
* child died |  |  |

The sample size is even: the sample median is defined to be the value halfway between the 25th and 26th observations. That is to say, it is obtained by splitting the difference between 1.820 (the 25th value) and 1.890 (the 26th value). This gives

½(1.820 + 1.890) = 1.855kg

## Activity 7: Birth weights of infants with SIRDS

Find the median birth weight for the infants who survived, and for those who did not.

## Answer

There were 23 children who survived the condition. Their birth weights are 1.130, 1.410, 1.575, 1.680, 1.715, 1.720, 1.760, 1.930, 2.015, 2.040, 2.090, 2.200, 2.400, 2.550, 2.570, 2.600, 2.700, 2.830, 2.950, 3.005, 3.160, 3.400, 3.640. The median birth weight for these children is 2.200 kg (the 12th value in the sorted list).

There were 27 children who died. The sorted birth weights are 1.030, 1.050, 1.100, 1.175, 1.185, 1.225, 1.230, 1.262, 1.295, 1.300, 1.310, 1.500, 1.550, 1.600, 1.720, 1.750, 1.770, 1.820, 1.890, 1.940, 2.200, 2.270, 2.275, 2.440, 2.500, 2.560, 2.730. The middle value is the 14th (thirteen either side) so the median birth weight for the children who died is 1.600 kg.

## Activity 8: Beta endorphin concentration (successful runners)

The first two columns of Table 4 give the blood plasma β endorphin concentrations of eleven runners before and after completing the Great North Run successfully. There is a marked difference between these concentrations. The data are reproduced in Table 10 below with the ‘After – Before’ differences also shown.

## Table 10 Differences in pre- and post-race βendorphin concentrations

Before | 4.3 | 4.6 | 5.2 | 5.2 | 6.6 | 7.2 | 8.4 | 9.0 | 10.4 | 14.0 | 17.8
After | 29.6 | 25.1 | 15.5 | 29.6 | 24.1 | 37.8 | 20.2 | 21.9 | 14.2 | 34.6 | 46.2
Difference | 25.3 | 20.5 | 10.3 | 24.4 | 17.5 | 30.6 | 11.8 | 12.9 | 3.8 | 20.6 | 28.4

Find the median of the ‘After – Before’ differences given in Table 10.

## Answer

The ordered differences are 3.8, 10.3, 11.8, 12.9, 17.5, 20.5, 20.6, 24.4, 25.3, 28.4, 30.6. The median difference is 20.5 pmol/l.

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