Mode & Median of grouped data

Question

The following are daily wages in shs of 30 workers of a flower farm. 

140, 108, 142, 139, 129, 116, 126, 144, 123, 114, 148, 104, 100, 134, 95, 88, 63, 80, 62, 69, 85, 77, 148, 106, 99, 132, 123, 103, 118, 133.

The flower farm gives bonuses of shs 10, 15, 20, 25, 30 and 35 for individuals in the respective salaries; exceeding 60 but not exceeding 75, exceeding 75 but not exceeding 90 and so on up to exceeding 135 but not exceeding 150. 

 

Required: 

1)Find median wage and median mode

2)Find modal wage and modal bonus 

Answer 1

Hi Wambui,

 

Before I begin, I'm assuming there's a typo in your question and the first part of the question should read "find the median wage and median bonus".

 

To begin, let's put the wages in numerical order

62, 63, 69, 77, 80, 85, 88, 95, 99, 100, 103, 104, 106, 108, 114, 116, 118, 123, 123, 126, 129, 132, 133, 134, 139, 140, 142, 144, 148, 148

 

The median (middle) wage is 115 [(114+116)/2].  There are two modes, 123 and 148, since both these wages appear twice and the others only appear once.

 

Now let's look at the bonuses.  I'm going to line salaries up with bonuses, with the bonuses in parentheses.

 

62 (10), 63 (10), 69 (10), 77 (15), 80 (15), 85 (15), 88 (15), 95 (20), 99 (20), 100 (20), 103 (20), 104 (20), 106 (25), 108 (25), 114 (25), 116 (25), 118 (25), 123 (30), 123 (30), 126 (30), 129 (30), 132 (30), 133 (30), 134 (30), 139 (35), 140 (35), 142 (35), 144 (35), 148 (35), 148 (35)

 

Below I've deleting the salaries and just showing the bonuses.

10, 10, 10, 15, 15, 15, 15, 20, 20, 20, 20, 20, 25, 25, 25, 25, 25, 30, 30, 30, 30, 30, 30, 30, 35, 35, 35, 35, 35, 35

 

There are 3 10s, 4 15s, 5 20s, 5 25s, 7 30s and 6 35s.

The median value is 25.

The modal value is 30.