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Your Turn 12th patient is in the group of five patients who are 67″ tall. The
It’s now a new day in the doctor’s office in which you median is therefore 67″.
intern, and you want to see if this morning’s patients are The mode is the value that occurs most frequently. There are five
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generally taller or shorter than yesterday’s patients. You patients who are 67″ Because the data fit into a normal distribu-
arrange the 23 patients’ heights in a data table, and then tion, as shown in the graph below the mean, median, and mode
graph the data. are all the same value.

Height (inches) Number of patients Mean
5
64 2 Median
Mode
65 3 4
66 4 Number of patients 3
67 5 2
68 4
1
69 3
0
70 2 64 65 66 67 68 69 70
Height of patients (inches)

5
2. To use the equation to determine the standard deviation, we
Number of patients 3 Then we square that difference. Let’s put these numbers in a table
first need to find the difference between each value and the mean.
4
to make things easier to see.
2

1 Height Number of Difference between Difference
(inches) patients height (inches) squared
and mean (67″)
0
64 65 66 67 68 69 70
64 2 3 9
Height of patients (inches)
65 3 2 4
1. What is the mean, median, and mode of this dataset, and where 66 4 1 1
are these points on the graph? 67 5 0 0

2. What is the standard deviation for this dataset? Draw it on the 68 4 -1 1
graph. 69 3 -2 4

70 2 -3 9
Solution
1. The mean is the sum of all of the heights, divided by
the number of patients. Remember, the height in the first Multiple patients have the same height. Therefore, to calculate
column of the table must be multiplied by the number of the sum of the squares of the differences, we need to look in the
people with that height, shown in the second column of the column that lists the number of patients at each height. We then
table. multiply the difference squared for each height by the number of
patients at each height, as follows:
(2 × 64″) + (3 × 65″) + (4 × 66″) + (5 × 67″) + (4 × 68″) +
(3 × 69″) + (2 × 70″) = 1541″ Sum = (2 × 9) + (3 × 4) + (4 × 1) + (5 × 0) + (4 × 1) +
(3 × 4) + (2 × 9) = 68
Then divide the sum by the number of patients, 23.
Substituting numbers into the equation, where n = number of
1541″ ÷ 23 = 67″ patients (23), we get:

The mean is 67″. − ) x 2
s = ∑(x i
To find the median, find the middle point of the data. The data n − 1
are written out in ascending order in the data table. In a sample
of 23 patients, the median height is the height of the 12th patient. = 68 = 68 = 3.09 = 1.76 ″
If you add the number of patients in the right column, the 23 − 1 22
TUTORIAL 1 STATISTICS 23

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