MDM2U1: Unit # 5– Lesson #5
Name:
Measures of Spread – Around the Median (2.6)
Warm-up:
1. The masses of 3-lb boxes of Chocolate labelled with a mass of 3 lb. were
checked by finding the masses of 128 boxes. The results are shown at the
right. Calculate the median.
Mass (lb)
2.7–2.8
2.8–2.9
2.9–3.0
3.0–3.1
3.1–3.2
Frequency
12
22
29
62
3
Lesson:
The measures of ______________________ can tell us about central values of data, however we also want to know how
the data clusters around these centres.
Measures of ___________________________ are quantities that indicate how closely the data clusters around the
center. There are different measures of spread. (Around the Median - inter-quartile range)
Quartiles - divide the set of ordered data into four groups with equal numbers of values; similar to a median that divides
the data into two equal groups. There are three dividing lines in order to get quartiles.
Q2 (aka the median). Q1 is the median of the lower half of the data, Q3 is the medians of the upper half of the data.
2. The mass of a 2-kg box of chocolates was checked by finding the masses of
150 boxes.
The results are shown in the table at the right.
a) Calculate the Median.
b) Calculate Q1 and Q3.
Mass (kg)
1.97
1.98
1.99
2.00
2.01
2.02
2.03
2.04
Frequency
8
15
19
35
33
22
14
4
Interquartile range  the range of the middle half of the data (does not necessarily fall in the middle of the
spectrum). The larger the range, the greater the spread of the central half of the data. This provides a good
measure of spread.
3. The table at the right gives the distribution of the number of hours per
week of Internet surfing.
a) Determine each of the following:
i) Q1, Median and Q3
Interval
(hours)
Frequency
0–3
5
3–6
11
6–9
18
9–12
22
12–15
25
15–18
15
18–21
9
ii) the inter-quartile range
b) A second set of data found a median of 13.8 h, and inter-quartile
range of 5 h. Compare the two sets of data with regard to central
tendency and spread.
MDM2U1: Unit # 5– Lesson #5
Name:
Semi interquartile range  is ½ of the interquartile range. This tells us how closely the data clusters around the
median.
An outlier is a piece of data that falls significantly __________ of the majority of data. One common method to
identify the outliers is to draw a box and whisker plot for a set of data and look at the inter-quartile range (the
difference between the first quartile and the third quartile.)
•
Generally, if a piece of data is 1.5 times the inter-quartile range away from the box, they are considered to be
an outlier
4. The following is a box and whisker plot for the weight of NBA players.
a) Approximately, what is the inter-quartile range?
b) Would 300 pounds be an outlier?
c) Would 150 pounds be an outlier?
5. a) Construct a box and whisker plot manually. Use it to identify the outlier. (Include: the minimum, the first quartile,
the Median, the third quartile, the Maximum).
145, 198, 154, 166, 159, 163, 120, 169, 199, 152, 167, 184, 156, 160
b) Verify using the graphing calculator (TI-83plus)
Homework: Pg. 148 #2, 3, 4, 6bcd, 7bd, 8b, 9b, 12