Answered

At IDNLearn.com, find answers to your most pressing questions from experts and enthusiasts alike. Our platform provides accurate, detailed responses to help you navigate any topic with ease.

The number of hours worked by each of the employees last week at two stores are listed below.

\begin{tabular}{|l|l|}
\hline \multicolumn{2}{|c|}{Hours Worked in a Week at Two Stores} \\
\hline Store 1 & [tex]$16,28,36,40,78$[/tex] \\
\hline Store 2 & [tex]$22,27,33,36,40$[/tex] \\
\hline
\end{tabular}

Which statements are true and supported by the data in the table? Check all that apply.

A. The data for Store 1 shows greater variability.
B. The median number of hours worked for the two stores is the same.
C. The mean of the data for Store 1 is greater than the mean of the data for Store 2.
D. The interquartile range of both data sets is the same.
E. The range of the data for Store 1 is less than the range of the data for Store 2.

Sagot :

GinnyAnsweridn
Certainly! Let's analyze the given data step-by-step:

### Store 1 Hours: [tex]\(16, 28, 36, 40, 78\)[/tex]
### Store 2 Hours: [tex]\(22, 27, 33, 36, 40\)[/tex]

First, let's compute the relevant statistical measures for each store.

#### Mean (Average):
- Store 1 Mean:
[tex]\[ \text{Mean} = \frac{16 + 28 + 36 + 40 + 78}{5} = \frac{198}{5} = 39.6 \][/tex]

- Store 2 Mean:
[tex]\[ \text{Mean} = \frac{22 + 27 + 33 + 36 + 40}{5} = \frac{158}{5} = 31.6 \][/tex]

#### Median (Middle Value):
- Store 1 Median:
[tex]\[ \text{Median} = 36 \quad \text{(middle value in sorted list)} \][/tex]

- Store 2 Median:
[tex]\[ \text{Median} = 33 \quad \text{(middle value in sorted list)} \][/tex]

#### Range (Difference between max and min):
- Store 1 Range:
[tex]\[ \text{Range} = 78 - 16 = 62 \][/tex]

- Store 2 Range:
[tex]\[ \text{Range} = 40 - 22 = 18 \][/tex]

#### Interquartile Range (IQR):
- Store 1 IQR:
[tex]\[ \text{IQR} = Q3 - Q1 = 46 - 34 = 12 \][/tex]
(where [tex]\(Q1\)[/tex] is the 25th percentile and [tex]\(Q3\)[/tex] is the 75th percentile)

- Store 2 IQR:
[tex]\[ \text{IQR} = Q3 - Q1 = 36 - 27 = 9 \][/tex]
(where [tex]\(Q1\)[/tex] is the 25th percentile and [tex]\(Q3\)[/tex] is the 75th percentile)

#### Variance (measure of variability):
- Store 1 Variance:
[tex]\[ \text{Variance} = 435.84 \][/tex]

- Store 2 Variance:
[tex]\[ \text{Variance} = 41.04 \][/tex]

### Conclusions Based on the Measurements:
1. The data for store 1 shows greater variability.
- True, because the variance for Store 1 (435.84) is much higher than for Store 2 (41.04).

2. The median number of hours worked for the two stores is the same.
- False, because the median for Store 1 is 36 hours, while the median for Store 2 is 33 hours.

3. The mean of the data for store 1 is greater than the mean of the data for store 2.
- True, because the mean for Store 1 (39.6) is greater than the mean for Store 2 (31.6).

4. The interquartile range of both data sets is the same.
- False, because the IQR for Store 1 is 12, while the IQR for Store 2 is 9.

5. The range of the data for store 1 is less than the range of the data for store 2.
- False, because the range for Store 1 (62) is greater than the range for Store 2 (18).

### Final Supported Statements:
- The data for store 1 shows greater variability.
- The mean of the data for store 1 is greater than the mean of the data for store 2.

So, the final true statements supported by the data are:
1. The data for store 1 shows greater variability.
2. The mean of the data for store 1 is greater than the mean of the data for store 2.
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.