Question

Using the following stem & leaf plot, find the five number summary for the data by hand. 1|7 7 2|2 6 6 3|2 6 4|2 6 9 9 5|8 8 8 9 9 6|1 2 Min= ______ Q1=_______ Med=______ Q3=_______ Max=______

Answer 1

Converting the data from the stem and leaf plot

17, 17,22,26,26,32,36,42,46,49,49, 58,58,58,59,59,61,62

Total observations18

The 5 number summary Is 1) Lowest Value 2) Q1 3) Median 4) Q3 and 5) Largest Value

1) Lowest Value = 17

2) Q1: For this we see that since n = 18, the middle values are the 9th and 10th values, which are 46 and 49

The values to the left of 46 are 17, 17,22,26,26,32,36,42, Q1 means average of the middle 2 terms of these 8 observations = Average of 4th and 5th terms = (26+26)/2 = 26

3) The median: Since n = 18, therefore the median is the average of the middle 2 values which is average of the 9th and 10th values = (46+49)/2 = 95/2 = 47. 5

4) Q3: The values to the right of 49 are 49,58,58,58,59,59,61,62 Q3 means means average of the middle 2 terms of these 8 observations = Average of 4th and 5th terms = (58+59)/2 =58.5 So Q3 = 58.5

5) The largest value = 62