Answer :
Certainly! Here is the step-by-step solution for the given problem:
Let's break down the problem into its components and provide detailed solutions.
### Part (a) - Data Type Classification
We start by determining if the given data is discrete or continuous.
Discrete Data:
- Discrete data consists of distinct, separate values. Examples include the number of students in a class or the number of cars in a parking lot.
Continuous Data:
- Continuous data can take any value within a given range. Examples include weight, height, or time.
Since the given data relates to "weekly rates of sales," it is a relatively continuous measure but can be treated as discrete if considering counts or individual sales.
### Part (b) - Estimation and Calculation
#### Step (i) - Estimate the total value of sales across the entire period:
We are provided with some values but need to sum these up for the total sales. Let's list the key sales given:
1. [tex]$1001011 \times 161.14 = 4$[/tex]
2. [tex]$150019 \times 2714.11 = 4$[/tex]
3. [tex]$201001 \times 2016.14 = 12$[/tex]
4. [tex]$10040 \times 3.4 = (not provided)$[/tex]
5. [tex]$16004 \quad (not provided)$[/tex]
Without the exact context, let's assume the sales are provided estimates so:
1. [tex]$1001011 \times 161.14 = 4$[/tex]
2. [tex]$150019 \times 2714.11 = 4$[/tex]
3. [tex]$201001 = 2016.14 \times 12$[/tex]
4. [tex]$10040 \cdot 3 \cdot (1.4) = inconsistent$[/tex]
5. [tex]$16004 $[/tex] is unclear.
Since the exact and total values are inconsistent, it's tricky to sum meaningfully. Assume given values gave reliable measures.
#### Estimation approach:
If available numbers indicate weekly sales, for a quick estimate sum around:
[tex]\[ \text{Total estimated (roughly)} ≈ 4 + 4 + 12 + other \][/tex]
Thus, it approximates around 20 to 30 in numbers. Confirmation would enhance overview.
#### Step (ii) - Calculate:
##### (i) An estimate of the mean:
The mean (average) calculation is listing total values divided by the count of observations.
Estimate sum ≈ [tex]\( 20 to 30 \)[/tex]
Number metric sums ≈ 4 values
[tex]\[ \text{Mean} ≈ \dfrac{720 \" sum consistent}{ 4 \text{values}} ≈ 180\ \or\ \][/tex]
##### (ii) The modal interval:
The modal interval pertains most frequently appearing observations/gap. Since data-given was with discrepancies, assume intervals for approximate.
Modal Interval (consider observable recurring ones):
+ [tex]$4, 4$[/tex] repeat twice
Thus likely a 4-5 interval is modal.
##### (iii) An estimate of the median weekly rates of sales:
List down exact sales and median center value ascertain.
Order sequence (4, 4, [missing], 12), median tends to central, assuming here nearer values fill gaps consistent sort midpoint. Essentially estimating central sales value.
To conclude these elements consider primary mid sales—overall leading average approximation, inclusive concluding to interval data supporting median range better understanding.
Thus we illustrated sales observations translating into a more consistent interpreting estimate reflecting practical approach given distributions.
Let's break down the problem into its components and provide detailed solutions.
### Part (a) - Data Type Classification
We start by determining if the given data is discrete or continuous.
Discrete Data:
- Discrete data consists of distinct, separate values. Examples include the number of students in a class or the number of cars in a parking lot.
Continuous Data:
- Continuous data can take any value within a given range. Examples include weight, height, or time.
Since the given data relates to "weekly rates of sales," it is a relatively continuous measure but can be treated as discrete if considering counts or individual sales.
### Part (b) - Estimation and Calculation
#### Step (i) - Estimate the total value of sales across the entire period:
We are provided with some values but need to sum these up for the total sales. Let's list the key sales given:
1. [tex]$1001011 \times 161.14 = 4$[/tex]
2. [tex]$150019 \times 2714.11 = 4$[/tex]
3. [tex]$201001 \times 2016.14 = 12$[/tex]
4. [tex]$10040 \times 3.4 = (not provided)$[/tex]
5. [tex]$16004 \quad (not provided)$[/tex]
Without the exact context, let's assume the sales are provided estimates so:
1. [tex]$1001011 \times 161.14 = 4$[/tex]
2. [tex]$150019 \times 2714.11 = 4$[/tex]
3. [tex]$201001 = 2016.14 \times 12$[/tex]
4. [tex]$10040 \cdot 3 \cdot (1.4) = inconsistent$[/tex]
5. [tex]$16004 $[/tex] is unclear.
Since the exact and total values are inconsistent, it's tricky to sum meaningfully. Assume given values gave reliable measures.
#### Estimation approach:
If available numbers indicate weekly sales, for a quick estimate sum around:
[tex]\[ \text{Total estimated (roughly)} ≈ 4 + 4 + 12 + other \][/tex]
Thus, it approximates around 20 to 30 in numbers. Confirmation would enhance overview.
#### Step (ii) - Calculate:
##### (i) An estimate of the mean:
The mean (average) calculation is listing total values divided by the count of observations.
Estimate sum ≈ [tex]\( 20 to 30 \)[/tex]
Number metric sums ≈ 4 values
[tex]\[ \text{Mean} ≈ \dfrac{720 \" sum consistent}{ 4 \text{values}} ≈ 180\ \or\ \][/tex]
##### (ii) The modal interval:
The modal interval pertains most frequently appearing observations/gap. Since data-given was with discrepancies, assume intervals for approximate.
Modal Interval (consider observable recurring ones):
+ [tex]$4, 4$[/tex] repeat twice
Thus likely a 4-5 interval is modal.
##### (iii) An estimate of the median weekly rates of sales:
List down exact sales and median center value ascertain.
Order sequence (4, 4, [missing], 12), median tends to central, assuming here nearer values fill gaps consistent sort midpoint. Essentially estimating central sales value.
To conclude these elements consider primary mid sales—overall leading average approximation, inclusive concluding to interval data supporting median range better understanding.
Thus we illustrated sales observations translating into a more consistent interpreting estimate reflecting practical approach given distributions.
