Do Now 1/30/12Do Now 1/30/12

Copy HW in your planner.Copy HW in your planner.Text p. 278, #1-13 all, #20 & 21Text p. 278, #1-13 all, #20 & 21

In your notebook, put the following In your notebook, put the following heading on the top of the page. heading on the top of the page. Section 7.1 “Mean, Median, Mode, and Section 7.1 “Mean, Median, Mode, and

Range”Range”

Chapter 7 “Collecting, Displaying, Chapter 7 “Collecting, Displaying, and Analyzing Data”and Analyzing Data”

Section 7.1 “Mean, Median, Mode, and Range”

Section 7.2 “Box-and-Whisker Plots”

Section 7.3 “Populations and Samples

ObjectiveObjective

SWBAT find the mean, median, and mode SWBAT find the mean, median, and mode of a set of numbers and data. of a set of numbers and data.

Section 7.1, “Mean, Median, Mode, and Range Section 7.1, “Mean, Median, Mode, and Range

the measures used to the measures used to represent the “middle” of a data represent the “middle” of a data set. There are 3 types: set. There are 3 types: (1) Mean (2) Median (3) Mode

Central TendencyCentral Tendency

RangeRangethe difference between the the difference between the

greatest and least values greatest and least values

FINDING A MEANFINDING A MEANTo find the To find the MEANMEAN of a set of numbers, add the of a set of numbers, add the numbers and divide the sum by how many numbers and divide the sum by how many numbers are in the set. numbers are in the set.

MEANMEAN is another word for is another word for AVERAGEAVERAGE. .

Computing MeansComputing MeansSally Joe from Idaho, is a big-time bowler. Sally Joe from Idaho, is a big-time bowler.

She bowled three games with the following She bowled three games with the following scores: scores:

197, 188, 182197, 188, 182

What is her mean score?What is her mean score?

197 + 188 + 182 3

567 3

189==

This is Sally Jo’sAVERAGE or MEAN

Try It Out!!Try It Out!!Find the mean of the dataFind the mean of the data

1) 6, 10, 12, 8, 141) 6, 10, 12, 8, 14

2) 97, 88, 822) 97, 88, 82

3) 45, 16, 72, 543) 45, 16, 72, 54

1) 6 + 10 + 12 + 8 + 14 = 50 = 101) 6 + 10 + 12 + 8 + 14 = 50 = 10

5 5 5 5

2) 97+88+82 = 267 = 892) 97+88+82 = 267 = 89

3 3 3 3

3) 45 +16 + 72 + 54 = 187 = 46.753) 45 +16 + 72 + 54 = 187 = 46.75

4 4 4 4

FINDING A MEDIANFINDING A MEDIANTo find the To find the MEDIANMEDIAN of a set of numbers, first write the of a set of numbers, first write the numbers numbers in order.in order. The median is the The median is the middlemiddle numbernumber or or the the mean of the two middle numbersmean of the two middle numbers. .

Even amount of # in setEven amount of # in set Odd amount of # in setOdd amount of # in set

MEDIANMEDIAN the middle number in a set of data. the middle number in a set of data.

Finding the MedianFinding the MedianFind the median age of Sally Sue’s family of 7.

41, 32, 36, 17, 41, 51, 32

Put the list IN ORDER than locate the MIDDLE #.MIDDLE #. 17, 32, 32, 3636, 41, 41, 51

Find the median age of Sally Moe’s family of 6. 41, 32, 36, 22, 51, 32

Put the list IN ORDER than find the MEAN of the MIDDLE 2 #s.MEAN of the MIDDLE 2 #s. 22, 32, 32,32, 3636, 41, 51

32 + 36 = 68/2 = 3434

FINDING A MODEFINDING A MODETo find the To find the MODEMODE of a set of numbers, first write of a set of numbers, first write the numbers in order. The mode is the number the numbers in order. The mode is the number that appears most often. that appears most often.

MODEMODE the most often number in a set of data.the most often number in a set of data.

Finding the ModeFinding the Mode

Find the mode of the following test scores in the class. 80, 88, 89, 90, 92, 90, 87, 90, 100, 84, 90

Put the list IN ORDER, the mode is the number thatappears the MOST often.MOST often.

80, 84, 87, 88, 89, 90, 90, 90, 9090, 90, 90, 90, 92, 100

OutlierOutlieran extreme value in a set of an extreme value in a set of

data that is much greater or less data that is much greater or less than the other values in the set than the other values in the set

Describing Data BestDescribing Data Best

the data are spread fairly evenlythe data are spread fairly evenly

the data set has an outlierthe data set has an outlier

the data involve a subject in which the data involve a subject in which many data points of one value are many data points of one value are important, such as election resultsimportant, such as election results

meanmean

median median

modemode

Most Useful WhenMost Useful WhenMeasureMeasure

Interpreting DataInterpreting DataThe line plot shows the number of miles 21 members of the The line plot shows the number of miles 21 members of the

cross-country team ran in a week. Find the mean, median, and cross-country team ran in a week. Find the mean, median, and mode from the line plot below. Which measure of central tendency mode from the line plot below. Which measure of central tendency best describes the data?best describes the data?

44 55 66 77

xx xxxxxx

xx

xxxx

xxxx

xxxx

xx

xxxx

xx

33

xxxxxx

88 99 1010 1111

xxxx

xx

Mean = 6.14Mean = 6.14 Median = 6Median = 6 Mode = 8Mode = 8The mean best describes the data because it is spread fairly even. 10 runners ran more than 6 miles and 10 runners ran less than 10 miles.

Exploring the Effects of Exploring the Effects of Outliers on Measures of Outliers on Measures of

Central TendencyCentral TendencyThe data shows Sara’s scores for the last 5

math tests: 88, 90, 55, 94, and 89. Identify the outlier in the data set. Then determine how the outlier affects the mean, median, and mode of the data. Then tell which measure of central tendency best describes the data with the outlier.

outlier 55

55, 88, 89, 90, 94

With the Outlier…With the Outlier… outlier 55

55, 88, 89, 90, 94

55+88+89+90+94 = 416

416 ÷ 5 = 83.2

The mean is 83.2.

55, 88, 89, 90, 94

The median is 89. There is no mode.

mean: median: mode:

Without the Outlier…Without the Outlier… 55, 88, 89, 90, 94

88+89+90+94 = 361

361 ÷ 4 = 90.25

The mean is 90.25.

88, 89, 90, 94

The median is 89.5. There is no mode.

mean: median: mode:

+2

= 89.5

HomeworkHomework

Text p. 278, #1-13 all, #20 & 21Text p. 278, #1-13 all, #20 & 21

Find the median and mode for the Find the median and mode for the following sets of data. following sets of data.

1)1) 1, 1, 2, 2, 2, 4, 4, 4, 4, 6, 7, 8, 91, 1, 2, 2, 2, 4, 4, 4, 4, 6, 7, 8, 9

2)2) 2, 7, 4, 9, 2, 5, 6, 11, 9, 4, 8, 102, 7, 4, 9, 2, 5, 6, 11, 9, 4, 8, 10

3)3) 14, 22, 33, 21, 87, 90, 43, 54, 55, 11, 22, 1214, 22, 33, 21, 87, 90, 43, 54, 55, 11, 22, 12

4)4) 10, 100, 1000, 99, 999, 3, 33, 333, 10, 3, 910, 100, 1000, 99, 999, 3, 33, 333, 10, 3, 9

1) Median = 4Mode = 4

2) Median = 6.5 Mode = 2,4,9

3) Median= 27.5 Mode = 22

4) Median = 33 Mode = 3,10

2, 2, 4, 4, 5, 6, 7, 8, 9, 9, 10, 11

11, 12, 14, 21, 22, 11, 12, 14, 21, 22, 22, 33,22, 33, 43, 54, 55, 87, 90 43, 54, 55, 87, 90

3, 3, 9, 10, 10, 3, 3, 9, 10, 10, 33,33, 99, 100, 333, 999, 1000 99, 100, 333, 999, 1000