On the right are the numbers of customers served by a restaurant on 40 consecutive days. (The numbers have been ranked lowest to highest.) Find the 2nd decile, 41 46 47 50 51 51 53 54 54 54 D 61 61 62 62 63 63 64 64 64 65 66 66 66 67 67 67 68 68 69 69 The number of customers representing the 2nd decile is 70 70 71 71 72 74 77 77 81 85
On the right are the numbers of customers served by a restaurant on 40 consecutive days. (The numbers have been ranked lowest to highest.) Find the 2nd decile, 41 46 47 50 51 51 53 54 54 54 D 61 61 62 62 63 63 64 64 64 65 66 66 66 67 67 67 68 68 69 69 The number of customers representing the 2nd decile is 70 70 71 71 72 74 77 77 81 85
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Understanding the Calculation of the 2nd Decile**
In the list below, you'll find the numbers of customers served by a restaurant over 40 consecutive days. These numbers have been ranked from the lowest to the highest. The task is to find the 2nd decile of this dataset.
**Customer Counts Over 40 Days:**
41, 46, 47, 50, 51, 51, 51, 53, 54, 54, 54,
61, 61, 62, 62, 63, 63, 64, 64, 64, 65,
66, 66, 66, 67, 67, 67, 68, 68, 69, 69,
70, 70, 71, 71, 72, 74, 77, 77, 81, 85
### How to Calculate the 2nd Decile
1. **Total Data Points**: There are 40 customer counts.
2. **Position of the 2nd Decile**:
- The position of the 2nd decile in an ordered dataset is found using the formula:
\[
D_k = \frac{k \times (N + 1)}{10}
\]
- For the 2nd decile, \( k = 2 \) and \( N = 40 \). Therefore:
\[
D_2 = \frac{2 \times (40 + 1)}{10} = \frac{82}{10} = 8.2
\]
3. **Interpreting the Position**:
- Since 8.2 is not a whole number, the 2nd decile is between the 8th and 9th value in the ordered list. You can find the integer portion at the 8th position and the decimal portion through linear interpolation if necessary.
- In this case, the 8th and 9th values are 53 and 54, respectively. The 2nd decile would be slightly above 53.
**Conclusion**: The number of customers representing the 2nd decile is approximately 53, indicating that 20% of the observed days had fewer than or equal to 53 customers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc8968af-ed75-41dd-a990-a36ece2bbe7e%2F4c4dbbaf-9358-462d-ad90-2772bbb4dc2a%2Ffv7l89_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding the Calculation of the 2nd Decile**
In the list below, you'll find the numbers of customers served by a restaurant over 40 consecutive days. These numbers have been ranked from the lowest to the highest. The task is to find the 2nd decile of this dataset.
**Customer Counts Over 40 Days:**
41, 46, 47, 50, 51, 51, 51, 53, 54, 54, 54,
61, 61, 62, 62, 63, 63, 64, 64, 64, 65,
66, 66, 66, 67, 67, 67, 68, 68, 69, 69,
70, 70, 71, 71, 72, 74, 77, 77, 81, 85
### How to Calculate the 2nd Decile
1. **Total Data Points**: There are 40 customer counts.
2. **Position of the 2nd Decile**:
- The position of the 2nd decile in an ordered dataset is found using the formula:
\[
D_k = \frac{k \times (N + 1)}{10}
\]
- For the 2nd decile, \( k = 2 \) and \( N = 40 \). Therefore:
\[
D_2 = \frac{2 \times (40 + 1)}{10} = \frac{82}{10} = 8.2
\]
3. **Interpreting the Position**:
- Since 8.2 is not a whole number, the 2nd decile is between the 8th and 9th value in the ordered list. You can find the integer portion at the 8th position and the decimal portion through linear interpolation if necessary.
- In this case, the 8th and 9th values are 53 and 54, respectively. The 2nd decile would be slightly above 53.
**Conclusion**: The number of customers representing the 2nd decile is approximately 53, indicating that 20% of the observed days had fewer than or equal to 53 customers.
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