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Statistics Ms. Silver asks her students to keep track of how many hours they spend on a semester project. The data below are from a simple random sample of the responses. Find the mean and the standard deviation of these data. 3.4 4.7 2.1 5.4 5.1 3.8 4.4 5.2 4.1 3.8 The mean, x , is the sum of all the data values divided by the number of data values. You can use sigma notation to express the calculation. The mean is 4.2 h. Recall that deviations are the signed differences between the data values and the mean. The standard deviation, s, is the sum of the squares of the deviations divided by one less than the number of data values. The standard deviation is about 1 h. The histogram shows the heights of students in a sample of kindergartners. Calculate the percentile ranks for children of heights 105 cm and 115 cm. Recall that the percentile rank of a value is the percentage of values in a data set that are below it. First make a table of counts to find the number in the sample. Then use this total to determine the percentage in each bin. To find the percentile of height 105 cm, add the percents in the bins below 105. That is, 105 is at the 8.3 + 12.5= 20.8th percentile. Height 115 cm is at the 8.3+ 12.5+ 33.3 +37.5 ≈ 91.7th percentile.