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The daily temperatures in New York City and Sacramento during 10 consecutive days are shown in the table. Which conclusion is true based on the given information?

\begin{tabular}{|c|c|}
\hline New York City ( [tex]$\left.{ }^{\circ} F \right)$[/tex] & Sacramento ( [tex]$\left.{ }^{\circ} F \right)$[/tex] \\
\hline 57 & 68 \\
\hline 51 & 72 \\
\hline 26 & 75 \\
\hline 42 & 73 \\
\hline 55 & 77 \\
\hline 46 & 80 \\
\hline 36 & 82 \\
\hline 39 & 75 \\
\hline 36 & 76 \\
\hline 49 & 73 \\
\hline
\end{tabular}

A. Because the interquartile range of the data for New York City is less than the interquartile range of the data for Sacramento, the variability in temperature in New York City is lower.

B. Because the interquartile range of the data for New York City is greater than the interquartile range of the data for Sacramento, the variability in temperature in New York City is greater.

C. Because the mean temperature in New York City is higher than the mean temperature in Sacramento, the variability in temperature in New York City is greater.

D. Because the mean temperature in New York City is lower than the mean temperature in Sacramento, there is less variability in temperature in New York City.

E. Because the median temperature in New York City is greater than the median temperature in Sacramento, the variability in temperature in New York City is greater.



Answer :

GinnyAnswer
To determine the variability in temperatures for New York City (NYC) and Sacramento, we need to calculate the interquartile range (IQR) for each city. The IQR is the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a data set. It measures the range within which the middle 50% of the data lie.

First, we are given daily temperature data for NYC and Sacramento:
- New York City temperatures: [57, 51, 26, 42, 55, 46, 36, 39, 36, 49]
- Sacramento temperatures: [68, 72, 75, 73, 77, 80, 82, 75, 76, 73]

By organizing this data, the interquartile ranges (IQR) have been computed as follows:

1. Calculation of IQR for New York City:
- 25th percentile (Q1): The value below which 25% of the data fall.
- 75th percentile (Q3): The value below which 75% of the data fall.
- For NYC temperatures, the IQR is 13.75.

2. Calculation of IQR for Sacramento:
- 25th percentile (Q1): The value below which 25% of the data fall.
- 75th percentile (Q3): The value below which 75% of the data fall.
- For Sacramento temperatures, the IQR is 3.75.

Now we compare the IQRs:
- NYC IQR: 13.75
- Sacramento IQR: 3.75

Since the IQR for NYC is greater than the IQR for Sacramento (13.75 > 3.75), the variability in temperatures in NYC is greater than in Sacramento.

Based on the calculated IQRs, the correct conclusion is:
B. Because the interquartile range of the data for New York City is greater than the interquartile range of the data for Sacramento, the variability in temperature in New York City is greater.

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