30 points (branliest) - takiya recorded the heights of two sets of plants, one set planted in the shade and one set planted in full sun. her data are shown in the plots below. which best explains the variability of the sets? the shaded plants set has greater variability because more data is clustered around the median. the sets are equally variable because the ranges of the data sets are equal. the full sun plants set has greater variability because the iqr for full sun plants is greater. the full sun plants set has greater variability because the median for full sun plants is greater.

Variability is the measure of the variation of a data set from the center. The mean and the median are the qualities that measure the center of a distribution.

For the first option, if more data is clustered around the median, (the measure of center), then the distribution has less variability than when less data is clustered around the median. Therefore, the first answer option is not correct because if more data is clustered around the median in the shaded plants set, then the shaded plant set will have less variability.

For the second option, the range is a measure of variability which measures the spread of the data set from the least value to the greatest value, but it does not take into account the variability of the other data values of the data set. Thus the range is regarded as a weak measure of variability and is not used when other measures of variability are available. Therefore, the second option is not correct.

For the third option, the inter-quartile range (IQR) is a better measure of variability than the range because it takes into account more data points than the range. Now, because, the full sun plants set has a greater IQR, this shows that they have greater variability. Therefore, the third option is the correct answer.

For the fourth option, the median is not a measure of variability. Thus, that a data set has a greater median than another data set does not mean that the data set would have a greater variability. Therefore, the fourth option is not the correct answer.

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