According to *The Wall Street Journal*, a start-up company’s ability to gain funding is a key to success. The funds raised (in millions of dollars) by  start-up companies follow. Click on the datafile logo to reference the data.

The datafile logo.

81

61

103

166

168

80

51

130

77

78

69

119

81

60

20

73

50

110

21

60

192

18

54

49

63

91

272

58

54

40

47

24

57

78

78

154

72

38

131

52

48

118

40

49

55

54

112

129

156

31

**a.** Construct a stem-and-leaf display. If your answer is zero, enter "".

 
 
 
 
 
 
 
 
 
 

**b.** Comment on the display.

The majority of the start-up companies in this set have - Select your answer -less thanmore thanItem 78  million in venture capital. Of the  start-up companies sampled,  have more than  million.


### Solution to Part (a): Constructing a Stem-and-Leaf Display

To create a stem-and-leaf display, separate the tens (stem) and units (leaf) values from each data point. Here’s the display:

#### Stem-and-Leaf Display (in millions of dollars)
```
1 | 8
2 | 0 1 4 4 7
3 | 1 8
4 | 0 0 7 8 9 9
5 | 0 1 2 4 4 4 5 7 8 9
6 | 0 0 1 3 9
7 | 2 3 7 8 8 8
8 | 0 1 1 3
9 | 1 2 8
10 | 3
11 | 0 8 9
12 | 9
13 | 0 1
15 | 4 6
16 | 6 8
19 | 2
27 | 2
```

In this display:
- Each stem represents tens of millions.
- Each leaf shows the units for values in that range.

### Solution to Part (b): Comment on the Display

- **Majority of Data**: The display reveals that most start-up companies have funding values concentrated around the lower end of the spectrum, particularly between $50 million and $80 million.
- **Data Distribution**: The majority of start-up companies in this data set have **less than 78 million** in venture capital. 
- **Companies with More than 78 Million**: There are **15** companies that raised more than 78 million dollars.

Would you like further details on the solution, or do you have any questions?

---

### Follow-Up Questions

1. What conclusions can be drawn from data skewness in a stem-and-leaf display?
2. How would the distribution change if we only included companies with over 100 million in funding?
3. Can a stem-and-leaf plot reveal potential outliers in venture capital data?
4. What other graphical representations could complement this data analysis?
5. How might funding amounts correlate with other variables, such as industry or company age?

---

### Tip
Using a stem-and-leaf plot is helpful when working with small-to-medium data sets because it retains the original data values while visually displaying the distribution.

According to *The Wall Street Journal*, a start-up company’s ability to gain funding is a key to success. The funds raised (in millions of dollars) by start-up companies follow: 81, 61, 103, 166, 168, 80, 51, 130, 77, 78, 69, 119, 81, 60, 20, 73, 50, 110, 21, 60, 192, 18, 54, 49, 63, 91, 272, 58, 54, 40, 47, 24, 57, 78, 78, 154, 72, 38, 131, 52, 48, 118, 40, 49, 55, 54, 112, 129, 156, 31.

Construct a stem-and-leaf display. Comment on the display: 'The majority of the start-up companies in this set have - Select your answer -less thanmore thanItem 78 million in venture capital. Of the start-up companies sampled, have more than million.'

Explore a data analysis example with a stem-and-leaf plot of start-up funding amounts, ranging from 18 to 272 million dollars. This exercise demonstrates data organization, distribution insights, and interpretation of descriptive statistics. Suitable for Grades 8-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation