# Office a 22 31 21 49 26 42 42 30 28 31 39 39 office b

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Office A: 22 31 21 49 26 42 42 30 28 31 39 39 Office B: 20 37 32 36 35 33 45 47 49 38 28 48 Ex. 2 Below are times obtained from a mail-order company's shipping records concerning time from receipt of order to delivery (in days) for items from their catalogue? 3 7 10 5 14 12 6 2 9 22 25 11 5 7 12 10 22 23 14 8 5 4 7 13 27 31 13 21 6 8 3 10 19 12 11 8 Homework: Day 1: pg 46 – 48 problems 1-5 Day 2: pg 55-58 problems 8-12 and pg 64 – 66 problem 16

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Chapter 1: Exploring Data Section 1.2: Describing Distributions with Numbers Knowledge Objectives: Students will: Explain what is meant by a resistant measure . Give two reasons why we use squared deviations rather just average deviations from the mean. Explain what is meant by degrees of freedom . Construction Objectives: Students will be able to: Identify situations in which the mean is the most appropriate measure of center and situations in which the median is the most appropriate measure. Given a data set: Find the quartiles . Find the five-number summary . Compute the mean and median as measures of center . Compute the interquartile range (IQR). Use the 1.5 × IQR rule to identify outliers. Compute the standard deviation and variance as measures of spread . Identify situations in which the standard deviation is the most appropriate measure of spread and situations in which the interquartile range is the most appropriate measure. Explain the effect of a linear transformation of a data set on the mean, median, and standard deviation of the set. Use numerical and graphical techniques to compare two or more data sets. Vocabulary: Boxplot – graphs the five number summary and any outliers Degrees of freedom – the number of independent pieces of information that are included in your measurement Five-number summary – the minimum, Q1, Median, Q3, maximum Interquartile range (IQR) – IQR = Q3 – Q1 Linear transformation – changes the data in the form of x new = a + bx Mean – the average value Median – the middle value (in an ordered list) Mode – the most frequent data value Outlier– a data value that lies outside the interval [Q1 – 1.5 × IQR, Q3 + 1.5 × IQR] P th percentile – p percent of the observations (in an ordered list) fall below at or below this number Quartile – multiples of 25 th percentile (Q1 – 25 th ; Q2 –50 th or median; Q3 – 75 th ) Range – difference between the largest and smallest observations Resistant measure – a measure (statistic or parameter) that is not sensitive to the influence of extreme observations Standard Deviation– the square root of the variance Variance – the average of the squares of the deviations from the mean Key Concepts: Measure of Central Tendency Computation Interpretation When to use Mean μ = (∑x i ) / N x‾ = (∑x i ) / n Center of gravity Data are quantitative and Median Arrange data in ascending order and divide the data set into half Divides into bottom 50% and top 50% Mode Tally data to determine most frequent observation Most frequent observation Center : The mean and the median are the most common measures of center Distributions Parameters Skewed Left:
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