With the stem and leaf plot given:
1 2
2 5 8
3 0 2 4
4 9
5 6 8 8 9
6 0 5 5 5 9
7 5 8
So,
12
25 28
30 32 34
49
56 58 58 59
60 65 65 65 69
75 78
(a) We are to find the median.
To find the median we need to arrange the data in ascending orders.
12, 25, 28, 30, 32, 34, 49, 56, 58, 58, 59, 60, 65, 65, 65, 69, 75, 78
recall the median is the middle number
Since we have a total of 18 numbers which is an even number, the median will lie between two numbers, that means we get the two numbers in the middle and divide by 2.
Median = 58 + 58
2
Median = 116/2
Medan = 58
(b) We are to find the mode
Recall the mode of a set of data is the number with the highest frequency, that is the number that appears more frequently.
So, from the stem and leaf plot, the number that appears more frequency is 65
Therefore, the Mode = 65
(c) We are to find the difference between the most expensive and the least expensive lamps
From the stem and leaf plot:
Most expensive lamp is $78
Least expensive lamp is $12
Therefore, the difference is by subtracting the least expensive from the most expensive:
= $78 - $12
= $66
Therefore, the difference between the most expensive and the least is expensive lamp is $66
(d) We are to find the number of lamps that cost more than $20 and less than $40.
They are: 25, 28, 30, 32, 34
Therefore, there are 5 lamps that cost more $20 and less than $40.
(e) We are to find the ratio of the lamps that cost less than $40 to the the lamps that cost more than $40.
The number of lamps that cost less than $40 are:
12, 25, 28, 30, 32, 34 = 6
The number of lamps that cost more than $40 are:
49, 56, 58, 58, 59, 60, 65, 65, 65, 69, 75, 78 = 12
Therefore, the ratio = 6 : 12
= 1 : 2