Question: 1. Find the mean, median and mode for each set of numbers. a. {34, 47, 12, 36, 26, 34, 28, 26, 48}…

1. Find the mean, median and mode for each set of numbers. a. {34, 47, 12, 36, 26, 34, 28, 26, 48} (4 marks)

b. {21, 23, 26, 34, 21, 29, 36, 45, 32, 26, 28, 26} (5 marks)

c. {8, 6, 2, 4, 7, 6, 2, 5, 3, 7, 9, 7} (5 marks)

Solution

Problem 1a Set: {34, 47, 12, 36, 26, 34, 28, 26, 48} Step 1: Calculate the Mean \[ \text{Mean} = \frac{34 + 47 + 12 + 36 + 26 + 34 + 28 + 26 + 48}{9} \] \[ \text{Mean} = \frac{291}{9} = 32.33 \] Step 2: Calculate the Median First, arrange the numbers in ascending order: \[ 12, 26, 26, 28, 34, 34, 36, 47, 48 \] Since there are 9 numbers, the median is the 5th number: \[ \text{Median} = 34 \] Step 3: Determine the Mode The numbers 26 and 34 both appear twice, which is more frequent than the other numbers. \[ \text{Mode} = 26, 34 \] --- Problem 1b Set: {2123, 26, 34, 2129, 36, 45, 32, 26, 28, 26} Step 1: Calculate the Mean \[ \text{Mean} = \frac{2123 + 26 + 34 + 2129 + 36 + 45 + 32 + 26 + 28 + 26}{10} \] \[ \text{Mean} = \frac{26 + 26 + 26 + 28 + 32 + 34 + 36 + 45 + 2123 + 2129}{10} = \frac{4865}{10} = 486.5 \] Step 2: Calculate the Median First, arrange the numbers in ascending order: \[ 26, 26, 26, 28, 32, 34, 36, 45, 2123, 2129 \] Since there are 10 numbers, the median is the average of the 5th and 6th numbers: \[ \text{Median} = \frac{32 + 34}{2} = 33 \] Step 3: Determine the Mode The number 26 appears three times, which is more frequent than the other numbers. \[ \text{Mode} = 26 \] --- Problem 1c Set: {8, 6, 24, 7, 6, 25, 3, 7, 9, 7} Step 1: Calculate the Mean \[ \text{Mean} = \frac{8 + 6 + 24 + 7 + 6 + 25 + 3 + 7 + 9 + 7}{10} \] \[ \text{Mean} = \frac{8 + 6 + 24 + 7 + 6 + 25 + 3 + 7 + 9 + 7}{10} = \frac{106}{10} = 10.6 \] Step 2: Calculate the Median First, arrange the numbers in ascending order: \[ 3, 6, 6, 7, 7, 7, 8, 9, 24, 25 \] Since there are 10 numbers, the median is the average of the 5th and 6th numbers: \[ \text{Median} = \frac{7 + 7}{2} = 7 \] Step 3: Determine the Mode The number 7 appears three times, which is more frequent than the other numbers. \[ \text{Mode} = 7 \]