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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.
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