Example (the formula for the mode):- Calculate the mode of the following frequency distributionValue FrequencyAt least Less than10 25 625 40 1940 55 1255 70 770 85 3{Answer:- 34.75}Exercise 2(p 256):- An analysis of sales invoices outstanding at the end of February is as follows:Invoice value Number ofinvoicesAt least Less thanRs. Rs.10 25 425 40 840 55 1855 70 970 85 3{Answer:- Rs. 47.89}Example (the median p258):- Find median of the following values:(i) 8, 6, 9, 12, 15, 6, 3, 20, 11.(ii) 8, 6, 7, 2, 1, 11, 3, 2, 5, 2{Answer:- (i) 9 , (ii) 3 }Example (median of an ungrouped frequency distribution):- Find the median of an ungrouped frequencydistributionValue X 8 12 16 17 19Frequency f 3 7 12 8 5{Answer:- 16}Example (the median of a grouped frequency distribution):- The average monthly earning of 135employees of Honda Ltd. Have been analyzed as a grouped frequency distribution as follows:Average monthly earnings Number ofinvoicesMore than Not more thanRs. Rs.120 140 12140 160 49160 180 25180 200 18200 220 17220 240 14Calculate the median monthly earnings of employees of Honda Ltd.{Answer:- Rs. 165.60}Exercise 3(p 260):- The following grouped frequency distribution gives the annual wages of 200 employeesin an engineering firm.WagesRs.Number of employees5000 and less than 5500 45500 and less than 6000 266000 and less than 6500 1336500 and less than 7000 357000 and less than 7500 2Calculate mean, median and mode of annual wages.{Answer:- Mean = Rs. 6262.50 Median = Rs. 6263.16 Mode = Rs. 6260.98}
Question
Example (the formula for the mode):- Calculate the mode of the following frequency distributionValue FrequencyAt least Less than10 25 625 40 1940 55 1255 70 770 85 3{Answer:- 34.75}Exercise 2(p 256):- An analysis of sales invoices outstanding at the end of February is as follows:Invoice value Number ofinvoicesAt least Less thanRs. Rs.10 25 425 40 840 55 1855 70 970 85 3{Answer:- Rs. 47.89}Example (the median p258):- Find median of the following values:(i) 8, 6, 9, 12, 15, 6, 3, 20, 11.(ii) 8, 6, 7, 2, 1, 11, 3, 2, 5, 2{Answer:- (i) 9 , (ii) 3 }Example (median of an ungrouped frequency distribution):- Find the median of an ungrouped frequencydistributionValue X 8 12 16 17 19Frequency f 3 7 12 8 5{Answer:- 16}Example (the median of a grouped frequency distribution):- The average monthly earning of 135employees of Honda Ltd. Have been analyzed as a grouped frequency distribution as follows:Average monthly earnings Number ofinvoicesMore than Not more thanRs. Rs.120 140 12140 160 49160 180 25180 200 18200 220 17220 240 14Calculate the median monthly earnings of employees of Honda Ltd.{Answer:- Rs. 165.60}Exercise 3(p 260):- The following grouped frequency distribution gives the annual wages of 200 employeesin an engineering firm.WagesRs.Number of employees5000 and less than 5500 45500 and less than 6000 266000 and less than 6500 1336500 and less than 7000 357000 and less than 7500 2Calculate mean, median and mode of annual wages.{Answer:- Mean = Rs. 6262.50 Median = Rs. 6263.16 Mode = Rs. 6260.98}
Solution
The questions you've posted are asking for the calculation of statistical measures such as mode, median, and mean. Here's how you can calculate each of these:
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Mode: The mode is the value that appears most frequently in a data set. To calculate the mode, you simply count the frequency of each value and the one with the highest frequency is the mode.
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Median: The median is the middle value in a data set when the values are arranged in ascending or descending order. If the data set has an odd number of observations, the median is the middle value. If the data set has an even number of observations, the median is the average of the two middle values.
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Mean: The mean, often referred to as the average, is calculated by adding up all the values in the data set and then dividing by the number of values.
For grouped data, the calculations are a bit more complex and involve finding the class interval with the highest frequency for the mode, and using the formula [(N/2) - F] / f * h + L for the median, where N is the total number of observations, F is the cumulative frequency of the class before the median class, f is the frequency of the median class, h is the class width, and L is the lower class boundary of the median class.
For the mean of grouped data, you use the formula ΣfX / Σf, where f is the frequency of each class and X is the midpoint of each class.
The answers provided for each example and exercise are the results of these calculations.
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