The shoe sizes of five students are: 10, 9, 11 and 4. Find the median shoe size, modal shoe size, and calculate the mean shoe size.

Mathematics
The shoe sizes of five students are: 10, 9, 11 and 4. Find the median shoe size, modal shoe size, and calculate the mean shoe size.

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Answer

9.5

(b) The median shoe size

Step 1: Arrange the shoe sizes in ascending order.
The shoe sizes are 10,9,11,910, 9, 11, 9.

9, 9, 10, 119, \, 9, \, 10, \, 11

Step 2: Determine the position for median.
Number of shoe sizes n=4n=4 (even).
Median is the average of the n2\frac{n}{2}th = 2nd and (n2+1)(\frac{n}{2}+1)th = 3rd values.

Step 3: Identify the values.
2nd value = 99
3rd value = 1010

Step 4: Calculate the median.

9+102=192=9.5\frac{9 + 10}{2} = \frac{19}{2} = 9.5

9.5

(c) Calculate the mean shoe size

Step 1: Calculate the sum of the shoe sizes.

9+9=189 + 9 = 18 18+10=2818 + 10 = 28 28+11=3928 + 11 = 39

Sum = 3939

Step 2: Count the number of shoe sizes.
n=4n = 4

Step 3: Calculate the mean.

394=9.75\frac{39}{4} = 9.75

9.75

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(b) The median shoe size Step 1: Arrange the shoe sizes in ascending order. The shoe sizes are 10, 9, 11, 9.

The shoe sizes of five students are: 10, 9, 11 and 4. Find the median shoe size, modal shoe size, and calculate the mean shoe size.
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
(b) The median shoe size Step 1: Arrange the shoe sizes in ascending order. The shoe sizes are 10, 9, 11, 9. 9, \, 9, \, 10, \, 11 Step 2: Determine the position for median. Number of shoe sizes n=4 (even). Median is the average of the (n)/(2)th = 2nd and ((n)/(2)+1)th = 3rd values. Step 3: Identify the values. 2nd value = 9 3rd value = 10 Step 4: Calculate the median. (9 + 10)/(2) = (19)/(2) = 9.5 9.5 (c) Calculate the mean shoe size Step 1: Calculate the sum of the shoe sizes. 9 + 9 = 18 18 + 10 = 28 28 + 11 = 39 Sum = 39 Step 2: Count the number of shoe sizes. n = 4 Step 3: Calculate the mean. (39)/(4) = 9.75 9.75