Statistics: Center, Spread & Plots

Step 1: Picture asking everyone: one student says $0\text{,}$ another $2\text{,}$ another $5\text{.}$

Step 2: The answers vary, so you would collect a data set.

Step 3: Yes, it is a statistical question.

Step 1: Add: $3 + 5 + 5 + 7 + 10 = 30\text{.}$

Step 2: Mean: split $30$ five ways, $\mathbf{6}\text{.}$

Step 3: Median: the list is in order, and the middle (third) value is $\mathbf{5}\text{.}$

Step 4: Mode: $5$ shows up twice, more than any other value, so the mode is $\mathbf{5}\text{.}$

Step 1: Range: $10 - 3 = \mathbf{7}\text{.}$

Step 2: Each value's distance from $6\text{:}$ $3, 1, 1, 1, 4\text{.}$

Step 3: Add: $3 + 1 + 1 + 1 + 4 = 10\text{.}$

Step 4: MAD: $10 \div 5 = \mathbf{2}\text{.}$ A typical value sits about $2$ from the mean.

Step 1: Count each bin: $0$ to $9$ has $3\text{,}$ $10$ to $19$ has $7\text{,}$ $20$ to $29$ has $4\text{.}$

Step 2: Check the total: $3 + 7 + 4 = 14$ students.

Step 3: Draw bars with heights $3\text{,}$ $7$ and $4\text{,}$ side by side with no gaps.

Step 4: The tallest bar says most students read $10$ to $19$ minutes.

Step 1: Minimum $4$ and maximum $25\text{.}$

Step 2: Median: the middle (fifth) value is $11\text{.}$

Step 3: Q1, the middle of the lower half $4, 6, 8, 9\text{:}$ $\tfrac{6 + 8}{2} = 7\text{.}$

Step 4: Q3, the middle of the upper half $12, 14, 16, 25\text{:}$ $\tfrac{14 + 16}{2} = 15\text{.}$

Step 1: Count and unit: $12$ waits, in minutes.

Step 2: Center: the median is $\tfrac{8 + 8}{2} = 8$ minutes.

Step 3: Spread: Q1 is $6$ and Q3 is $11\text{,}$ so the IQR is $5$ minutes.

Step 4: Unusual values: two students waited $24$ and $25$ minutes after a late bus.