4 Key ConceptThis section introduces measures that can be used to compare values from different data sets, or to compare values within the same data set. The most important of these is the concept of the z score.
5 Definition z Score (or standardized value) the number of standard deviations that a given value x is above or below the mean
6 Measures of Position z score SamplePopulationRound z to 2 decimal places
7 Interpreting Z ScoresWhenever a value is less than the mean, its corresponding z score is negativeOrdinary values: z score between –2 and 2 Unusual Values: z score < -2 or z score > 2
8 DefinitionQ1 (First Quartile) separates the bottom 25% of sorted values from the top 75%.Q2 (Second Quartile) same as the median; separates the bottom 50% of sorted values from the top 50%.Q1 (Third Quartile) separates the bottom 75% of sorted values from the top 25%.
9 divide ranked scores into four equal parts QuartilesQ1, Q2, Q3divide ranked scores into four equal parts25%Q3Q2Q1(minimum)(maximum)(median)
10 Find lower & upper Quartile To fined Q1, first calculate one-quarter of n and add ½ to obtain ¼ n + ½ . Round this to nearest integer.Examplen = 11,then ¼ n + ½ = ¼ (11)+½ = rounded off to 3Q1 = 2Q3 = 19Examplen = 12,then ¼ n + ½ = ¼ (12)+½ = then the Q1 in position 3 & 4 which is (5+6)/2=5.5Q2 in position 9 & 10 which is (21+23)/2=22
11 PercentilesJust as there are three quartiles separating data into four parts, there are 99 percentiles denoted P1, P2, P99, which partition the data into 100 groups.Percentile of value x = • 100number of values less than xtotal number of values
12 Converting from the kth Percentile to the Corresponding Data Value Notationn total number of values in the data setk percentile being used
13 Example 1 Find the percentile corresponding the weight of 0.8143 & find P10, P25Solution
14 Semi-interquartile Range: Some Other StatisticsInterquartile Range (or IQR): Q3 - Q1Semi-interquartile Range:2Q3 - Q1Midquartile:2Q3 + Q1Percentile Range: P90 - P10
15 Recap In this section we have discussed: z Scores z Scores and unusual valuesQuartilesPercentilesOther statistics
16 Exploratory Data Analysis (EDA) Section 3-5Exploratory Data Analysis (EDA)
17 Key ConceptThis section discusses outliers, then introduces a new statistical graph called a boxplot, which is helpful for visualizing the distribution of data.
18 Important PrinciplesAn outlier can have a dramatic effect on the mean.An outlier can have a dramatic effect on the standard deviation.An outlier can have a dramatic effect on the scale of the histogram so that the true nature of the distribution is totally obscured.
19 DefinitionsFor a set of data, the 5-number summary consists of the minimum value; the first quartile Q1; the median (or second quartile Q2); the third quartile, Q3; and the maximum value.A boxplot is a graph of a data set that consists of a line extending from the minimum value to the maximum value, and a box with lines drawn at the first quartile, Q1; the median; and the third quartile, Q3.
35 Which measure of center is the only one that can be used with data at the nominal level of measurement?MeanMedianMode
36 Which of the following measures of center is not affected by outliers? MeanMedianMode
37 Find the mode (s) for the given sample data. 79, 25, 79, 13, 25, 29, 56, 797948.142.525
38 Which is not true about the variance? It is the square of the standard deviation.It is a measure of the spread of data.The units of the variance are different from the units of the original data set.It is not affected by outliers.
39 Weekly sales for a company are $10,000 with a standard deviation of $450. Sales for the past week were $ This isUnusually high.Unusually low.About right.
40 In a data set with a range of 55. 1 to 102 In a data set with a range of 55.1 to and 300 observations, there are 207 data points with values less than Find the percentile for 88.6.32116.0369670
41 H.W 2Fine mean, median, mode, midrange, range, standard deviation, variance, P30Then draw the BoxplotAge of US President