Question

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

Answer 1

Answer:

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 ___frequency____relative frequency %

28.4_______1 __________1. 96

28.6_______2__________3.92

29.5_______1___________1.96

30.3_______1___________1.96

31.5_______2___________3.92

32.1_______1____________1.96

32.2_______1___________1.96

32.8_______1___________1.96

32.9_______2___________3.92

33________2___________3.92

33.3_______1___________1.96

35.4_______1___________1.96

35.5_______2___________3.92

36.1________1___________1.96

36.2_______2___________3.92

37.2_______7___________13.73

38.5_______1____________1.96

39.3_______1____________1.96

40.3_______1____________1.96

40.5_______1____________ 1.96

40.9_______1____________1.96

41.3_______1 ____________1.96

42.3______1_____________1.96

43.3______2____________ 3.92

44.2______1 _____________1.96

44.5______1 _____________1.96

44.6_____ 1 ______________1.96

45.3_____1 _______1.96

45.5_____2 ______3.92

45.9_____2 ______3.92

46______1 _______1.96

47.2_____1 _______1.96

49.8_____1 _______1.96

54.3____1________1.96

68.8____2________3.92

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