gaokao 2019 Q19

gaokao · China · national-II-arts 12 marks Measures of Location and Spread
19. (12 points) To understand the production situation of small and medium enterprises in the industry, a government department randomly surveyed 100 enterprises and obtained a frequency distribution table for the growth rate $y$ of production value in the first quarter compared to the previous year's first quarter.
Interval for $y$$[ - 0.20,0 )$$[ 0,0.20 )$$[ 0.20,0.40 )$$[ 0.40,0.60 )$$[ 0.60,0.80 )$
Number of enterprises22453147

(1) Estimate the proportion of enterprises with production value growth rate not less than $40\%$ and the proportion of enterprises with negative growth, respectively;
(2) Find the estimated values of the mean and standard deviation of the production value growth rate for this type of enterprise (use the midpoint of each interval as the representative value for data in that interval). (Accurate to 0.01)
Attachment: $\sqrt { 74 } \approx 8.602$ .
Solution:
19. (12 points)\\
To understand the production situation of small and medium enterprises in the industry, a government department randomly surveyed 100 enterprises and obtained a frequency distribution table for the growth rate $y$ of production value in the first quarter compared to the previous year's first quarter.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
Interval for $y$ & $[ - 0.20,0 )$ & $[ 0,0.20 )$ & $[ 0.20,0.40 )$ & $[ 0.40,0.60 )$ & $[ 0.60,0.80 )$ \\
\hline
Number of enterprises & 2 & 24 & 53 & 14 & 7 \\
\hline
\end{tabular}
\end{center}

(1) Estimate the proportion of enterprises with production value growth rate not less than $40\%$ and the proportion of enterprises with negative growth, respectively;\\
(2) Find the estimated values of the mean and standard deviation of the production value growth rate for this type of enterprise (use the midpoint of each interval as the representative value for data in that interval). (Accurate to 0.01)

Attachment: $\sqrt { 74 } \approx 8.602$ .\\