Unit 4 – Probability and Statistics Section 7.7 Day 9

Warm-Up P. 982 #5 - 12

Warm-Up Review 5) About 0.651 6) About 0.154 7) About 0.308 8) About 0.019 9) 0.5 10) About 0.265 11) About 0.505 12) About 0.145

Section 7.7 Statistics and Statistical Graphs Goal: Use measures of Central Tendency and Measures of Dispersion to describe data sets, and use box-and whisker plots to describe data graphically. Statistics – numerical values used to summarize and compare sets of data 2 Main Groups Measures of Central Tendency Measures of Dispersion (Variation)

Section 7.7 Statistics and Statistical Graphs MEASURES OF CENTRAL TENDENCY Mean – the sum of data values divided by the number of data values is a mean (average). Median – is the middle value of a data set. If the data set contains a even number of values, the median is the mean of the two middle numbers Mode – The most frequently occurring value in a set of data.

Example 1 Find the mean, median, and mode for the given data set. 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40, 24 Mean: Sum of the Terms 445 = Number of Terms 13 Mean: 34.2

Example 1 (cont.) Find the mean, median, and mode for the given data set. 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40, 24 Median: Arrange terms from lowest to highest 17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48 Median: 36

Example 1 (cont.) Find the mean, median, and mode for the given data set. 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40, 24 Mode: Number that appears the most 17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48 Mode: 40

Section 7.7 Statistics and Statistical Graphs Box-and-Whisker Plot – a box and whisker plot uses quartiles to form the center box and whiskers. Quartiles – separate a finite data set into four equal parts. Outlier – is an item of data with a substantially different value from the rest of the items in the data set.

Quartiles 71 58 56 63 84 74 85 82 86 78 65 58 56 58 58 63 65 71 74 78 82 84 85 86 Median of lower half Q1 = 60.5 Median of upper half Q3 = 83 58 + 63 82 + 84 = 60.5 = 83 2 2 Median of data set Q2 = 72.5 71 + 74 = 72.5 2

Box-and-Whisker Plot Q1 Q2 Q3 Maximum Minimum 56 60.5 72.5 83 86 50 60 70 80 90

Outlier 56 64 73 59 98 65 59 Find the mean, median, and mode of this data set. Is there an outlier in this set. If there is an outlier, remove it from the set and recalculate the mean, median, and mode. 67.71, 64, 59 YES; 98 62.67, 61.5, 59

Outlier Rules for outliers: Maximum > 1.5(Median) Minimum < ½(Median) Given the data set: 22 40 42 45 50 58 64 73 65 65 83 Is there an outlier in this set. YES; 22 Because: 22 < ½(58) 22 < 29

Measures of Dispersion (Variation) Definition Range Greatest Value – Least Value Interquartile Range Q3 – Q1 Standard Deviation Measure of how each data value in the set varies from the mean.

Measures of Variation 56 58 58 63 65 71 74 78 82 84 85 86 Median of lower half Q1 = 60.5 Median of upper half Q3 = 83 Median of data set Q2 = 72.5 What is the range for this data set? What is the interquartile range for this data set? 30 22.5

How to find Standard Deviation Find the mean of the data set. Find the difference between each data value and the mean. Square each difference. Find the mean (average) of the squares. Take the square root of the average. That is the standard deviation.

Data Set 56 58 58 63 65 71 74 78 82 84 85 86 Median of lower half Q1 = 60.5 Median of upper half Q3 = 83 Median of data set Q2 = 72.5 What is mean of this data set? 71.67

Standard Deviation Steps 2 & 3 x Mean Difference Squared Value 56 71.67 -15.67 245.55 58 -13.67 186.87 63 -8.67 74.17 65 -6.67 44.49 71 -0.67 0.45 74 2.33 5.43 78 6.33 40.07 82 10.33 106.71 84 12.33 152.03 85 13.33 177.69 86 14.33 205.35 SUM: 1425.28

10.9 is our Standard Deviation Step 4: Find the mean of the squares. Mean of the squares: 1425.28 12 = 118.77 Step 5: Take square root of the mean of squares. Sigma σ = sqrt(118.77) = 10.9 10.9 is our Standard Deviation

HOMEWORK P. 449 #4 – 7 ALL #11 – 27 ODD