Below is the data on the percentage of 25- to 34-year-olds in each of the 50 states and the District of Columbia, listed in alphabetical order, who had some type of postsecondary degree as of 2010: 31.5 32.9 33.0 28.6 37.2 43.3 45.9 37.2 68.8 36.2 35.5 31.5 32.9 33.0 28.6 37.2 43.3 45.9 37.2 68.8 36.2 35.5 40.5 37.2 45.3 36.1 45.5 42.3 33.3 30.3 37.2 45.5 54.3 37.2 49.8 32.1 39.3 40.3 44.2 28.4 46.0 47.2 32.8 32.2 38.5 44.5 44.6 40.9 29.5 41.3 35.4 a. Identify all the outliers. b. Construct a stem-and-leaf plot. c. Construct a relative frequency

Step-by-step explanation:

Given the following data:

31.5 32.9 33.0 28.6 37.2 43.3 45.9 37.2 68.8 36.2 35.5 31.5 32.9 33.0 28.6 37.2 43.3 45.9 37.2 68.8 36.2 35.5 40.5 37.2 45.3 36.1 45.5 42.3 33.3 30.3 37.2 45.5 54.3 37.2 49.8 32.1 39.3 40.3 44.2 28.4 46.0 47.2 32.8 32.2 38.5 44.5 44.6 40.9 29.5 41.3 35.4

Value ___frequencyrelative frequency %

28.41 1. 96

28.623.92

29.511.96

30.311.96

31.523.92

32.111.96

32.211.96

32.811.96

32.923.92

3323.92

33.311.96

35.411.96

35.523.92

36.111.96

36.223.92

37.2713.73

38.511.96

39.311.96

40.311.96

40.51 1.96

40.911.96

41.31 1.96

42.311.96

43.32 3.92

44.21 1.96

44.51 1.96

44.6 1 1.96

45.31 1.96

45.52 3.92

45.92 3.92

461 1.96

47.21 1.96

49.81 1.96

54.311.96

68.823.92

Lower outlier = Q1 - (1.5 × IQR)

Upper outlier = Q3 + (1.5 × IQR)

IQR = Interquartile range ;

Q1 = 1/4(n+1)th term

Q3 = 3/4(n+1)th term

IQR = Q3 - Q1

n = number of observations = 51

Q1 = (51 + 1)/4= 52/4 = 13 th term = 33

Q3 = 3(51 + 1) /4 = 156/4 = 39th term = 44.5

IQR = 44.5 - 33 = 11.5

LOWER OUTLIER = 33 - (1.5*11.5) = 33 - 17.25 = entries < 15.75

UPPER OUTLIER = 44.5 + (1.5*11.5) = 44.5 + 17.25 = 61.75

Entries > 61.75