Transcript 13.6 mean, median, mode checkpoint

TODAY IN ALGEBRA…
 Learning Target: 13.6 You will compare
measures of central tendency and
dispersion
 Independent Practice
 AT – Ch.9 Test corrections
13.6 MEASURES OF CENTRAL TENDENCY: MEAN, MEDIAN,
MODE
MEAN: average
𝑆𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠
=
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑒𝑟𝑚𝑠
MEDIAN: middle number
𝑝𝑢𝑡 𝑛𝑢𝑚𝑏𝑒𝑟 𝑖𝑛 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔 𝑜𝑟𝑑𝑒𝑟, 𝑎𝑛𝑑 𝑓𝑖𝑛𝑑 𝑚𝑖𝑑𝑑𝑙𝑒
𝑛𝑢𝑚𝑏𝑒𝑟
MODE: number that occurs the most
𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑟 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑡ℎ𝑎𝑡 𝑠ℎ𝑜𝑤 𝑢𝑝 𝑡ℎ𝑒 𝑚𝑜𝑠𝑡
13.6 MEASURES OF CENTRAL TENDENCY
EXAMPLE: Find the mean, median, and mode(s) of the data.
Cost (in dollars) of computer monitors:
296, 215, 426, 390, 351, 215, 289
MEAN: average = 296 + 215 + 426 + 390 + 351 + 215 + 289
7
2182
=
= 𝟑𝟏𝟏. 𝟕𝟏
7
MEDIAN: middle number
215, 215, 289, 296, 351, 390, 426
MODE: most frequent number 𝟐𝟏𝟓
13.6 MEAN, MEDIAN, MODE
EXAMPLE 2: Find the mean, median, and mode(s) of the data.
Heights (in feet) of waterfalls:
1000, 1000, 1181, 1191, 1200, 1268, 1328, 2584
MEAN: average =
1000 + 1000 + 1181 + 1191 + 1200 + 1268 + 1328 + 2584
8
10752
= 𝟏𝟑𝟒𝟒
=
8
MEDIAN: middle number
1000, 1000, 1181, 1191, 1200, 1268, 1328, 2584
If there are two “middle numbers” then take the average:
=
1191 + 1200
2
2391
=
2
= 𝟏𝟏𝟗𝟓. 𝟓
MODE: most frequent number 𝟏𝟎𝟎𝟎
13.6 MEAN, MEDIAN, MODE
CHECKPOINT: Complete problems Pg.877: 3-10
13.6 MEAN, MEDIAN, MODE
CHECKPOINT: Complete problems Pg.877: 3-10
MEAN =
=
1+1+1+2+3+3+5+5+6
27
9
=𝟑
9
MEAN =
=
MEDIAN:
1, 1, 1, 2, 3, 3, 5, 5, 6
MEDIAN:
MODE:
MODE:
1, 1, 1, 2, 3, 3, 5, 5, 6
9 + 10 + 12 + 15 + 16
5
62
= 𝟏𝟐. 𝟒
5
9, 10, 12, 15, 16
𝑁𝑂𝑁𝐸
13.6 MEAN, MEDIAN, MODE
CHECKPOINT: Complete problems Pg.877: 3-10
MEAN = 13 + 16 + 19 + 20 +8 22 + 25 + 30 + 31 MEAN = 14 + 15 + 15 + 14 + 14 + 16 + 18 + 15
8
176
121
= 8 = 𝟐𝟐
= 8 = 𝟏𝟓. 𝟏𝟑
MEDIAN:
MEDIAN:
13, 16, 19, 20, 22, 25, 30, 31 14, 14, 14, 15, 15, 15, 16, 18
15 + 15
20 + 22
=
𝟐𝟏
= 2
= 2 = 𝟏𝟓
MODE: 𝑁𝑂𝑁𝐸
MODE:
14, 14, 14, 15, 15, 15, 16, 18
𝟏𝟒 𝒂𝒏𝒅 𝟏𝟓
13.6 MEAN, MEDIAN, MODE
CHECKPOINT: Complete problems Pg.877: 3-10
MEAN =5.52 + 5.44 + 3.60 +65.76 + 3.80 + 7.22 MEAN = 300 + 320 + 341 + 348 + 360 + 333
6
31.34
2002
= 6 = 𝟓. 𝟐𝟐
= 6 = 𝟑𝟑𝟑. 𝟔𝟕
MEDIAN:
MEDIAN:
3.60, 3.80, 5.44, 5.52, 5.76, 7.22 300, 320, 333, 341, 348, 360
5.44 + 5.52
333 + 341
=
𝟑𝟑𝟕
=
𝟓.
𝟒𝟖
=
=
2
2
MODE: 𝑁𝑂𝑁𝐸
MODE: 𝑁𝑂𝑁𝐸
13.6 MEAN, MEDIAN, MODE
CHECKPOINT: Complete problems Pg.877: 3-10
MEDIAN:
0.3, 0.4, 0.7, 0.7, 0.8, 0.9, 1.0, 1.2, 1.6
To use the median, you must put
numbers in increasing order FIRST!
MEDIAN:
2, 3, 4, 4, 6, 6, 7, 8, 8
13.6 MEASURES OF CENTRAL TENDENCY: RANGE
RANGE: Difference of the greatest value from the least
value
= 𝑔𝑟𝑒𝑎𝑡𝑒𝑠𝑡 𝑛𝑢𝑚𝑏𝑒𝑟 − 𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 𝑛𝑢𝑚𝑏𝑒𝑟
EXAMPLE: Top ten finishing times for the 100 meter dash and
200 meter dash are listed below. Find the range of each set
of data.
A: 10.62, 10.94, 10.94, 10.98, 11.05, 11.13, 11.15, 11.28, 11.29, 11.32
𝑟𝑎𝑛𝑔𝑒 = 11.32 − 10.62 = 𝟎. 𝟕
B: 21.37, 21.40, 22.23, 22.23, 22.34, 22.34, 22.36, 22.60, 22.66, 22.73
𝑟𝑎𝑛𝑔𝑒 = 22.73 − 21.37 = 𝟏. 𝟑𝟔
13.6 MEASURE OF CENTRAL TENDENCY: RANGE
CHECKPOINT: Complete problems Pg.877: 11-16
Find the range of the data. Round to the nearest tenth.
13.6 MEASURE OF CENTRAL TENDENCY: RANGE
CHECKPOINT: Complete problems Pg.877: 11-16
Find the range of the data. Round to the nearest tenth.
𝑟𝑎𝑛𝑔𝑒 = 85 − 20
= 𝟔𝟓
𝑟𝑎𝑛𝑔𝑒 = 145 − 111
= 𝟑𝟒
𝑟𝑎𝑛𝑔𝑒 = 100 − 30
= 𝟕𝟎
𝑟𝑎𝑛𝑔𝑒 = 550 − 480
= 𝟕𝟎
𝑟𝑎𝑛𝑔𝑒 = 1.70 − 0.85
= 𝟎. 𝟖𝟓
𝑟𝑎𝑛𝑔𝑒 = 84.2 − 2.5
= 𝟖𝟏. 𝟕
EXIT TASK TO AT
(unless you have test corrections)
Pg. 878: 20
The population densities (in people per square mile) for
each of the 10 most densely populated states in 2003
were 719.0, 418.5, 315.6, 536.6, 820.6, 1164.6, 406.5,
275.9, and 1029.9.
Find the mean, median, mode and range of the data.