gaokao 2015 Q18

gaokao · China · national-II-arts Data representation
18. (This question is worth 12 points). A company randomly surveyed 40 users from regions $A$ and $B$ respectively to understand user satisfaction with its products. Based on user satisfaction scores, a frequency distribution histogram of user satisfaction scores in region $A$ and a frequency distribution table of user satisfaction scores in region $B$ were obtained.
Frequency Distribution Histogram of User Satisfaction Scores in Region A [Figure]
Satisfaction Score Interval\multicolumn{5}{|c|}{Frequency Distribution Table of User Satisfaction Scores in Region B}
Frequency$[ 50,60 )$$[ 60,70 )$$[ 70,80 )$$[ 80,90 )$$[ 90,100 ]$
2814106

(I) Draw the frequency distribution histogram of user satisfaction scores in region $B$ on the answer sheet, and compare the mean and dispersion of satisfaction scores in the two regions through this histogram (no need to calculate specific values, just provide conclusions); [Figure] (II) Based on user satisfaction scores, user satisfaction levels are divided into three categories:
Satisfaction ScoreBelow 7070 to 89At least 90
Satisfaction LevelDissatisfiedSatisfiedVery Satisfied

Estimate which region has a higher probability that a user's satisfaction level is dissatisfied, and explain the reasoning.
18. (This question is worth 12 points). A company randomly surveyed 40 users from regions $A$ and $B$ respectively to understand user satisfaction with its products. Based on user satisfaction scores, a frequency distribution histogram of user satisfaction scores in region $A$ and a frequency distribution table of user satisfaction scores in region $B$ were obtained.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Frequency Distribution Histogram of User Satisfaction Scores in Region A}
  \includegraphics[alt={},max width=\textwidth]{d02047a7-2e53-46f4-95bc-7a4508088779-3_593_1177_904_333}
\end{center}
\end{figure}

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
Satisfaction Score Interval & \multicolumn{5}{|c|}{Frequency Distribution Table of User Satisfaction Scores in Region B} \\
\hline
Frequency & $[ 50,60 )$ & $[ 60,70 )$ & $[ 70,80 )$ & $[ 80,90 )$ & $[ 90,100 ]$ \\
\hline
 & 2 & 8 & 14 & 10 & 6 \\
\hline
\end{tabular}
\end{center}

(I) Draw the frequency distribution histogram of user satisfaction scores in region $B$ on the answer sheet, and compare the mean and dispersion of satisfaction scores in the two regions through this histogram (no need to calculate specific values, just provide conclusions);\\
\includegraphics[max width=\textwidth, alt={}, center]{d02047a7-2e53-46f4-95bc-7a4508088779-3_554_1047_1939_340}\\
(II) Based on user satisfaction scores, user satisfaction levels are divided into three categories:

\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Satisfaction Score & Below 70 & 70 to 89 & At least 90 \\
\hline
Satisfaction Level & Dissatisfied & Satisfied & Very Satisfied \\
\hline
\end{tabular}
\end{center}

Estimate which region has a higher probability that a user's satisfaction level is dissatisfied, and explain the reasoning.\\