$\left.\begin{array}{c|c|c}\begin{array}{c}\text { Loub mies } \\ 50 \\ 45 ?\end{array} & \begin{array}{c}F \cdot I \\ 0-10 \\ 10-20\end{array} & \begin{array}{c}F \\ 20-30\end{array} \\ 38 \\ 26 \\ 10 \\ 4\end{array}\right)\left(\begin{array}{cc}5 \\ 30-40 & 16 \\ 40-50 & 6 \\ 50-60 & 4\end{array}\right.$
Answer (2)
Calculate the midpoints of the frequency intervals.
Calculate the weighted mean using the midpoints and frequencies: 95 2295 = 24.157894736842106 .
Estimate the missing 'Loub mies' value using the calculated mean.
The estimated missing 'Loub mies' value is 24.16 .
Explanation
Analyze the problem We are given a frequency distribution table with missing data. The goal is to estimate the missing 'Loub mies' value. The 'Loub mies' column seems to represent some measurement associated with the frequency intervals.
Calculate midpoints First, calculate the midpoint of each frequency interval (F.I.). The midpoint is the average of the lower and upper bounds of the interval.
List of midpoints The midpoints are calculated as follows:
0-10: ( 0 + 10 ) /2 = 5
10-20: ( 10 + 20 ) /2 = 15
20-30: ( 20 + 30 ) /2 = 25
30-40: ( 30 + 40 ) /2 = 35
40-50: ( 40 + 50 ) /2 = 45
50-60: ( 50 + 60 ) /2 = 55
Calculate weighted mean Next, calculate the weighted mean using the midpoints and corresponding frequencies. This will give us an estimate of the average value within the distribution.
Weighted mean calculation The weighted mean is calculated as: 5 + 38 + 26 + 16 + 6 + 4 ( 5 × 5 ) + ( 15 × 38 ) + ( 25 × 26 ) + ( 35 × 16 ) + ( 45 × 6 ) + ( 55 × 4 ) = 95 25 + 570 + 650 + 560 + 270 + 220 = 95 2295 = 24.157894736842106
Estimate missing value Since we don't have a clear relationship between the 'Loub mies' values and the frequency intervals, we can use the calculated mean as an estimate for the missing 'Loub mies' value. This assumes that the 'Loub mies' values are somewhat related to the distribution of the data.
Final Answer Therefore, the estimated missing 'Loub mies' value is approximately 24.16 .
Examples
In statistical analysis, estimating missing values is a common task. For example, if you're analyzing survey data and some respondents didn't answer a particular question, you can use methods like mean imputation to fill in the missing values. This ensures that your analysis can still use the incomplete data without significantly skewing the results. The weighted mean is particularly useful when dealing with grouped data, as it takes into account the frequency of each group.
To estimate the missing 'Loub mies' value, we calculate the midpoints of the given frequency intervals and then compute the weighted mean of those midpoints with their respective frequencies, resulting in an estimate of approximately 24.16. This value provides a representation of the average within the distribution. Therefore, the estimated missing 'Loub mies' value is approximately 24.16 .
;
