Question

Using the following stem & leaf plot, find the five number summary for the data by hand.

1|7 9
2|1 4 8
3|1 4
4|1 4 6 7
5|2 4 5 6 7
6|0 2

Min =
Q1 =
Med =
Q3 =
Max =

Answer 1

Five Summary:

Min = 17
Q1 = 28
Med = 45
Q3 = 55
Max = 62

Explanation:

To find Five Summary let us convert stem and leaf to normal data points

for 1| 7 9

we can write, 17 19

Similarly for 2| 1 4 8 we can write, 21,24,28

Similary, all data are.

17, 19, 21, 24 , 28, 31, 34, 41, 44, 46, 47, 52, 54, 55, 56, 57, 60, 62

Therefore, from data points

we can say,

Min = 17, Max = 62

n = 18 even therefore,

Median = Average of = (18/2 + 1)th +18/2th   = (10th term + 9th term)/2= (46+44)/2 = 45

To find Q1 and Q3 Place parentheses around the numbers above and below the median.

(17, 19, 21, 24 , 28, 31, 34, 41, 44), (46 47, 52, 54, 55, 56, 57, 60, 62)

Q1 as a median in the lower half of the data and think of Q3 as a median for the upper half of data.

(17, 19, 21, 24 , 28, 31, 34, 41 ,44), (46, 47, 52, 54, 55, 56, 57, 60, 62)

therefore Q1 = 28 , Q3 = 55

Subtract Q1 from Q3 to find the interquartile range.

IQR = 55 - 28 = 27