What is the range and mean of the weekly wages …

Mathematics Questions

What is the range and mean of the weekly wages paid to staff in a hotel: £245, £140, £525, £163, £195, £174, and £140?

Short Answer

The range of wages paid to staff is from £140 to £525, with a mean wage of £226. This was determined by identifying the minimum and maximum wage values and calculating the average based on the total sum of wages divided by the number of staff members.

Step-by-Step Solution

Range of wages is £140 to £525. Mean wage = £226.

Step 1: Determine the Range of Wages

The range of wages is calculated by identifying the minimum and maximum amounts in the data set. In this case, the weekly wages paid to staff are £245, £140, £525, £163, £195, £174, and £140. By examining these values:

  • Minimum wage = ¬¨¬£140
  • Maximum wage = ¬¨¬£525

Thus, the range of wages is from £140 to £525.

Step 2: Calculate the Mean Wage

The mean wage represents the average wage calculated by dividing the total sum of wages by the number of workers. To find this, sum up all the individual wages:

  • Sum of wages = ¬¨¬£245 + ¬¨¬£140 + ¬¨¬£525 + ¬¨¬£163 + ¬¨¬£195 + ¬¨¬£174 + ¬¨¬£140 = ¬¨¬£1582
  • Number of observations = 7 (total staff members)

Now, using the formula for mean:

Mean Wage = Total Sum of Wages / Number of Staff = £1582 / 7 = £226

Step 3: Present the Final Results

After calculating the range and mean, you can summarize the findings to provide a clear answer. The minimum wage is £140 while the maximum is £525, which shows the spread of wages. Furthermore, the average wage is calculated as £226:

  • Range of wages = ¬¨¬£140 to ¬¨¬£525
  • Mean wage = ¬¨¬£226

This concludes the analysis of the wages paid to staff.

Related Concepts

Range Of Wages

The difference between the maximum and minimum wages in a data set, indicating the spread of the wage values.

Mean Wage

The average value of a set of wages, calculated by dividing the total sum of wages by the number of entries.

Minimum And Maximum

The lowest (minimum) and highest (maximum) values in a data set, used to determine the range and provide context for data analysis.

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