Question

we do (part i)
8 min
display and interpret graphs using quantitative data including stem - and - leaf plots, line graphs, box plots.
use the following set of data to answer the following questions:
25 32 46 11 51 39 45 32 17 30
create a steam - and - leaf plot

1. what is the range of the data?
2. what is the mean of the data set?
3. what is the median of the data set?
4. what is the mode of the data?

Explanation:

Step1: Sort the data

11, 17, 25, 30, 32, 32, 39, 45, 46, 51

Step2: Create stem - and - leaf plot

Stem | Leaf
---|---
1 | 1 7
2 | 5
3 | 0 2 2 9
4 | 5 6
5 | 1

Step3: Calculate the range

The range is the difference between the maximum and minimum values. Range = 51 - 11 = 40

Step4: Calculate the mean

Mean $\bar{x}=\frac{11 + 17+25+30+32+32+39+45+46+51}{10}=\frac{328}{10}=32.8$

Step5: Calculate the median

Since there are 10 data points (an even number), the median is the average of the 5th and 6th ordered values. Median=$\frac{32 + 32}{2}=32$

Step6: Calculate the mode

The mode is the value that appears most frequently. The mode is 32 as it appears twice and other values appear only once.

Answer:

1. Stem - and - leaf plot:

Stem | Leaf
---|---
1 | 1 7
2 | 5
3 | 0 2 2 9
4 | 5 6
5 | 1

1. 40
2. 32.8
3. 32
4. 32