3-4 example12

# 3-4 example12 - Student Grady Simonton Course Math119...

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Unformatted text preview: Student: Grady Simonton Course: Math119: Elementary Statistics - Spring 2010 - CRN: 49239 Instructor: Shawn Parvini - 16 weeks Date: 2/18/10 Book: Triola: Elementary Statistics, 11e Time: 2:02 PM The following data represent the weights of 16 pre- 1964 quarters. Find the 5-number summary and construct a boxplot. 6.1487 6.1312 6.3276 6.0001 6.2720 6.1952 6.1183 6.2414 6.2863 6.0763 6.2148 6.1425 6.1723 6.1940 6.2643 6.0827 The 5-number summary consists of the smallest and largest numbers in the data set, the ﬁrst quartile, the median, and the third quartile. Be sure to ﬁrst list the data in ascending order. The data in ascending order are shown below. 6.0001 6.0763 6.0827 6.1183 6.1312 6.1425 6.1487 6.1723 6.1940 6.1952 6.2148 6.2414 6.2643 6.2720 6.2863 6.3276 From the list we see that the smallest number in the data set is 6.0001, and the largest number in the data set is 6.3276. Find the ﬁrst quartile, Q1. Remember that the ﬁrst quartile is the 25th percentile. Use the formula for the locator. L 2 [W] (n) , where k is the percentile and n is the number of values. L — i 16 — 4 _ 100 l ) Since L is a whole number, the percentile is midway between the 4th value and the next value in the sorted data set. Find Q1 by adding the 4th value and the 5th value and dividing the sum by 2. _ 6.1183+6.13l2 = 6.12475 2 Q1 Find the median, M. Remember that the median is the 50th percentile. L- i (16) — 8 100 Since L is a whole number, the percentile is midway between the 8th value and the next value in the sorted data set. Find M by adding the 8th value and the 9th value and dividing the sum by 2.The ordered list is repeated below for reference. 6.0001 6.0763 6.0827 6.1183 6.1312 6.1425 6.1487 6.1723 6.1940 6.1952 6.2148 6.2414 6.2643 6.2720 6.2863 6.3276 Page 1 Student: Grady Simonton Course: Math119: Elementary Statistics - Spring 2010 - CRN: 49239 Instructor: Shawn Parvini - 16 weeks Date: 2/18/10 Book: Triola: Elementary Statistics, 11e Time: 2:02 PM _ 6.1723+6.1940 2 M =6.18315 Now ﬁnd the third quartile, Q3. Remember that the third quartile is the 75th percentile. L—[—5] 16 —12 _ 100( )— Since L is a whole number, the percentile is midway between the 12th value and the next value in the sorted data set. Add the 12th and 13th values and divide the sum by 2. The ordered list is repeated below for reference. 6.0001 6.0763 6.0827 6.1183 6.1312 6.1425 6.1487 6.1723 6.1940 6.1952 6.2148 6.2414 6.2643 6.2720 6.2863 6.3276 _ 6.2414 + 6.2643 Q3 — = 6.25285 Thus, the 5-number summary is 6.0001, 6.12475, 6.18315, 6.25285, and 6.3276. Use the 5-number summary to construct the boxplot. There are two different types of boxplots, skeletal (or regular) and modiﬁed. If the data contains any outliers, then a modiﬁed boxplot is constructed, otherwise a skeletal boxplot is constructed. A data value is an outlier if it is above Q 3 by an amount greater than 1.5(IQR) or below Q1 by an amount greater than 1.5(IQR). First ﬁnd the interquartile range. IQR = Q3_Ql = 6.25285 —6.12475 = 0.12310 Now ﬁnd Q3 +1.5(IQR) and Q1 — 1.5(IQR). Q3 +1.5(IQR)= 6.25285 +1.5(0.12810)= 6.4450 Q1—1.5(IQR)=6.12475 — 1.5(0.12810) = 5.9326 Since the smallest number in the data set, 6.0001, is larger than 5.93 26, and the largest number in the data set, 6.3276, is smaller than 6.4450, there are no outliers. Since there are no outliers, construct a skeletal (or regular) boxplot. The steps to constructing this boxplot are given below. Page 2 Student: Grady Simonton Course: Math119: Elementary Statistics - Spring 2.010 - CRN: 49239 Instructor: Shawn Parvini - 16 weeks Date: 2/18/10 Book: Triola: Elementary Statistics, 11e Time: 2:02 PM - Construct a scale with values that include the minimum and maximum data values. . Construct a box (rectangle) extending from Q] to Q3, and draw a line in the box at the median value. - Draw lines extending outward from the box to the minimum and maximum data values. Using the S-number summary and the steps given above, the boxplot of the data is constructed. |—-—| ﬁrm—leijan—I— 5 5.1 6.2 6.3 Page 3 ...
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