Download Refreshing Your Skills 11

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.