Answer to Question #298347 in Statistics and Probability for Leyman

Question

After several months of planting roses, Siti measures the height in centimeters

each of the plant. The height of the plants is given as below:

38, 14, 22, 36, 35, 29,19, 24, 32, 35, 41, 47

a) Construct a stem-and-leaf diagram for Siti’s data.

b) Calculate the mean, median, mode and range for Siti’s data

Answer 1

a)

A stem and leaf plot is usually ordered, where the leaves are arranged in ascending order from the left to the right. The first digit of a number represents the stem while the second digit represents the leaf. Also, there is no need to separate the leaves (digits) with punctuation marks (commas, periods) since each leaf is always a single digit.

Thus the stem and leaf diagram can be expressed as below

stem leaf

1 4 9

2 2 4 9

3 2 5 5 6 8

4 1 7

From the diagram:

stem 1 represents class interval 10 to 19

stem 2 represents class interval 20 to 29

stem 3 represents class interval 30 to 39

stem 4 represents class interval 40 to 49

b) Calculate

the mean = (sum of values) / ( number of values)

this equals to ( 38+14+22+36+35+29+19+24+32+35+41+47 ) / ( 12 ) = (372)/(12) = 31

median= the middle score in a set of numbers

we arrange the data in ascending order as below

14,19,22,24,29,32,35,35,36,38,41,47

The median will be average of the 6th and 7th number = (32 +35) = 33.5

mode = most frequently occurring in a set of given numbers

From our data, the mode = 35

range = (greatest value) - ( smallest value) = (47 - 14) =33