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Year 10 Maths: Calculate Mode and Mean from a Bedroom Frequency Table
Mathematics
Grade 10 (Year 10)
Question Content
A council reviews the number of bedrooms in 40 houses located in the same area. The table shows the information gathered.\n| Number of bedrooms | Frequency |\n|----|----|\n| 1 | 2 |\n| 2 | 12 |\n| 3 | 13 |\n| 4 | 10 |\n| 5 | 3 |\na) Find the modal average number of bedrooms.\nb) Work out the mean number of bedrooms.
Correct Answer
a) 3; b) 3.1
Detailed Solution Steps
1
Step 1: Solve for part (a) (mode): The mode is the value with the highest frequency. Looking at the table, the number 3 has the highest frequency of 13, so the mode is 3.
2
Step 2: Solve for part (b) (mean): First, calculate the total number of bedrooms by multiplying each number of bedrooms by its frequency: (1×2) + (2×12) + (3×13) + (4×10) + (5×3) = 2 + 24 + 39 + 40 + 15 = 120.
3
Step 3: Divide the total number of bedrooms by the total number of houses (40) to get the mean: 120 ÷ 40 = 3.1.
Knowledge Points Involved
1
Mode (Modal Average)
The mode is a measure of central tendency that represents the most frequently occurring value in a data set. It is used when identifying the most common category or value, and a data set can have one mode (unimodal), multiple modes (bimodal/multimodal), or no mode if all values occur equally often.
2
Mean (Arithmetic Mean)
The mean is a measure of central tendency calculated by finding the sum of all data values (or the sum of each value multiplied by its frequency for grouped data) and dividing by the total number of data points. It is used to find a typical 'average' value that reflects the overall data set, but can be skewed by extreme values.
3
Frequency Table Data Analysis
A frequency table organizes data by listing distinct values and how often each occurs. It simplifies calculating measures of central tendency (mode, mean, median) by summarizing raw data, making it easier to interpret large data sets like the number of bedrooms in multiple houses.
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