Question

The height of 25 coffee shrubs in a certain farm in centimeters were recorded as below :
109 120 114 121 150
149 125 106 148 140
109 108 130 138 142
148 147 107 136 139
132 135 109 116 128
a). Illustrate this information on a frequency table using a class internal of 5 cm starting with
105 – 109.
b). what is the model class
c) Calculate the mean height.
d). calculate the median height.

Answer 1

a) Frequency Table:

Height Range (cm) | Frequency
105 - 109 | 3
110 - 114 | 2
115 - 119 | 2
120 - 124 | 2
125 - 129 | 2
130 - 134 | 2
135 - 139 | 3
140 - 144 | 2
145 - 149 | 2
150 - 154 | 1

b) The model class is the class with the highest frequency, which in this case is the class 105 - 109 cm.

c) Mean Height:
Sum of all heights = 109 + 120 + 114 + 121 + 150 + 149 + 125 + 106 + 148 + 140 + 109 + 108 + 130 + 138 + 142 + 148 + 147 + 107 + 136 + 139 + 132 + 135 + 109 + 116 + 128 = 3283
Mean height = Sum of all heights / Number of heights = 3283 / 25 = 131.32 cm

d) Median Height:
First, we need to arrange the heights in ascending order:
106, 107, 108, 109, 109, 109, 114, 116, 120, 121, 125, 128, 130, 132, 135, 136, 138, 139, 140, 142, 147, 148, 148, 149, 150

There are 25 heights, so the mean of the 12th and 13th, which are the middle values, will be the median.
Median height = (125 + 128) / 2 = 126.5 cm