Question

10. The scores in a class quiz are as follows: 58, 62, 62, 63, 65, 65, 65, 68, 69, 72, 72, 75, 76, 78, 79, 81, 84, 84, 85, 92, 94, 95, 98. a. Draw a box and whiskers diagram of the data set b. Determine if there are any outliers in the data set

Answer 1

Our sorted data is: 58, 62, 62, 63, 65, 65, 65, 68, 69, 72, 72, 75, 76, 78, 79, 81, 84, 84, 85, 92, 94, 95, 98 ) First Quartile is median of first half of data, i.e. first 11 terms 58, 62, 62, 63, 65, 65, 65, 68, 69, 72, 72 Clearly the First quartile or median of this first half of data is Q1- 65 Third Quartile is median of second half of data, .e. last 11 terms 76, 78, 79, 81, 84, 84, 85, 92, 94, 95, 98 y Clearly the Third quartile or median of this second half of data is Q3-84 And Q2 is median of complete data, Q275 The five number sum mmary is: Five Number Summ 58 65 Median (Q2) 75 84 98 ar Mimimum Q1 3 Maximum

Box AND WHISKER PLOT Median Minimum Maximum 75 58 98 65 84 60 70 80 90 100 Q1 Qs b) Interquartile range is IQR- Q3-Q1 19 IQR 19 Lower limit for outlier-Qi-1.5 * (Q3-Q) = 36.5 Upper limit for outlier Q3 + 1.5 * (Q3-Qi) = 112.5 Outliers are the points either below lower limit or above upper limits Outliers are: NONE