Question

Find the 5 number summary for the data shown

11	17
20	21
25	29
34	39
47	58
74	75
77	82

5 number summary(from least to greatest):

From the table below, give the percentile of a value of 48 (rounded to the nearest whole percentile)

83	48
28	111
68	105

48 represents the  -th percentile

Answer 1

solution:

the data given is as follows in the ascending order

11

17

20

21

25

29

34

39

47

58

74

75

77

82

number of data counts = n = 14

median = (n+1)/2 = (14+1)/2 = 7.5th item which lies between 7th and 8th data point so we will take the average of the 7th and 8th data point to get the meedian

median = (34+39)/2 = 36.5

Q1 = middle of first half of the data point = (7+1)/2 = 4th item

so Q1 = 21

Q3 = middle of second half of data point = 7+(7+1)/2 = 11th item

so Q3 = 74

mininum = 11

maximum = 82

so five number summary as follows:

min = 11

Q1 = 21

median = 36.5

Q3 = 74

max = 82

solution 2)

first of all arrange the given data in ascending order

28

48

68

83

105

111

we have to find the percentile of number 48

percentile = (number of data below the 48/ total number of data points)*100

percentile = (1/6)*100 = 16.67 = 17th percentile

so the data point 48 is represent the 17th percentile